82
Chapter 1 10 Glencoe Geometry Word Problem Practice Points, Lines, and Planes NAME ______________________________________________ DATE ____________ PERIOD _____ 1-1 1. STREETS The map shows some of the roads in downtown Little Rock. Lines are used to represent streets and points are used to represent intersections. Four of the street intersections are labeled. What street corresponds to line AB? 2. FLYING Marsha plans to fly herself from Gainsville to Miami. She wants to model her flight path using a straight line connecting the two cities on the map. Sketch her flight path on the map shown below. 3. MAPS Nathan’s mother wants him to go to the post office and the supermarket. She tells him that the post office, the supermarket and their home are collinear, and the post office is between the supermarket and their home. Make a map showing the three locations based on this information. 4. ARCHITECTURE An architect models the floor, walls, and ceiling of a building with planes. To locate one of the planes that will represent a wall, the architect starts by marking off two points in the plane that represents the floor. What further information can the architect give to specify the plane that will represent the wall? CONSTRUCTION For Exercises 5 and 6, use the following information. Mr. Riley gave his students some rods to represent lines and some clay to show points of intersection. Below is the figure Lynn constructed with all of the points of intersection and some of the lines labeled. 5. What is the intersection of lines k and n? 6. Name the lines that intersect at point C. 7. Are there 3 points that are collinear and coplanar? If so, name them. E F G C B H D A k m n p Tallahasee Jacksonville Gainsville Daytona Beach Orlando Tampa St. Petersburg Fort Lauderdale Miami 100 mi W. 20th St. A Asher Ave. 70 W. 29th St. Washington St. S. Ceder St. B C D Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

  • Upload
    buianh

  • View
    295

  • Download
    2

Embed Size (px)

Citation preview

Page 1: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 10 Glencoe Geometry

Word Problem PracticePoints, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-1

1. STREETS The map shows some of theroads in downtown Little Rock. Linesare used to represent streets and pointsare used to represent intersections. Fourof the street intersections are labeled.What street corresponds to line AB?

2. FLYING Marsha plans to fly herselffrom Gainsville to Miami. She wants tomodel her flight path using a straightline connecting the two cities on themap. Sketch her flight path on the mapshown below.

3. MAPS Nathan’s mother wants him to go to the post office and thesupermarket. She tells him that the post office, the supermarket and theirhome are collinear, and the post office is between the supermarket and theirhome. Make a map showing the threelocations based on this information.

4. ARCHITECTURE An architect modelsthe floor, walls, and ceiling of a buildingwith planes. To locate one of the planesthat will represent a wall, the architectstarts by marking off two points in theplane that represents the floor. Whatfurther information can the architectgive to specify the plane that willrepresent the wall?

CONSTRUCTION For Exercises 5 and 6,use the following information.Mr. Riley gave his students some rods torepresent lines and some clay to showpoints of intersection. Below is the figureLynn constructed with all of the points ofintersection and some of the lines labeled.

5. What is the intersection of lines kand n?

6. Name the lines that intersect at point C.

7. Are there 3 points that are collinear andcoplanar? If so, name them.

E

F

GC

BHD

A

k

m

n

pTallahasee Jacksonville

Gainsville Daytona Beach

OrlandoTampa

St. Petersburg

Fort Lauderdale

Miami

100 mi

W. 20th St.A

Asher Ave.

70W. 29th St.

Was

hing

ton

St.

S. C

eder

St.B

CD

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-56 Geo-01-873958 4/3/06 6:29 PM Page 10

Page 2: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 18 Glencoe Geometry

Word Problem PracticeLinear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-2

1. MEASURING Vera is measuring thesize of a small hexagonal silver box thatshe owns. She places a standard 12 inchruler alongside the box. About how longis one of the sides of the box?

2. WALKING Marshall lives 2300 yardsfrom school and 1500 yards from thepharmacy. The school, pharmacy, and hishome are all collinear, as shown in thefigure.

What is the total distance from thepharmacy to the school?

3. HIKING TRAIL A hiking trail is 20kilometers long. Park organizers want tobuild 5 rest stops for hikers with one oneach end of the trail and the other 3spaced evenly between. How muchdistance will separate successive reststops?

4. RAILROADS A straight railroad trackis being built to connect two cities. Themeasured distance of the track betweenthe two cities is 160.5 miles. Find theprecision for this measurement andexplain its meaning.

BUILDING BLOCKS For Exercises 5 and6, use the following information.Lucy’s younger brother has three woodencylinders. They have heights 8 inches, 4inches, and 6 inches and can be stacked oneon top of the other.

5. If all three cylinders are stacked one ontop of the other, how high will theresulting column be? Does it matter inwhat order the cylinders are stacked?

6. What are all the possible heights ofcolumns that can be built by stackingsome or all of these cylinders?

8 in. 4 in. 6 in.

School Pharmacy Home

1500 yards

2300 yards

2in. 1

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-56 Geo-01-873958 4/3/06 6:29 PM Page 18

Page 3: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 25 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeDistance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-3

1. CAMPGROUND Troop 175 is designingtheir new campground by first mappingeverything on a coordinate grid. Theyhave found a location for the mess halland for their cabins. They want thebathrooms to be halfway between thesetwo. What will be the coordinates of thelocation of the bathrooms?

2. PIZZA Calvin’s home is located at themidpoint between Fast Pizza and PizzaNow. Fast Pizza is a quarter mile awayfrom Calvin’s home. How far away isPizza Now from Calvin’s home? How farapart are the two pizzerias?

3. SPIRALS Caroline traces out the spiralshown in the figure. The spiral begins atthe origin. What is the shortest distancebetween Caroline’s starting point andher ending point?

4. WASHINGTON, D.C. The UnitedStates Capitol is located 800 meterssouth and 2300 meters to the east of theWhite House. If the locations wereplaced on a coordinate grid, the WhiteHouse would be at the origin. What isthe distance between the Capitol andthe White House? Round your answer tothe nearest meter.

MAPPING For Exercises 5 and 6, usethe following information.Ben and Kate are making a map of theirneighborhood on a piece of graph paper.They decide to make one unit on the graphpaper correspond to 100 yards. First, theyput their homes on the map as shown below.

5. How many yards apart are Kate’s andBen’s homes?

6. Their friend Jason lives exactly halfwaybetween Ben and Kate. Mark thelocation of Jason’s home on the map.

y

xO

Ben’s House

Kate’s House

y

xO

y

xO

Cabins

Mess Hall

Less

on

1-3

05-56 Geo-01-873958 4/3/06 6:29 PM Page 25

Page 4: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 33 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeAngle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-4

1. LETTERS Lina learned about types ofangles in geometry class. As she waswalking home she looked at the letterson a street sign and noticed how manyare made up of angles. The sign shelooked at was KLINE ST. Which letter(s)on the sign have an obtuse angle? Whatother letters in the alphabet have anobtuse angle?

2. SQUARES A square has four rightangle corners. Give an example ofanother shape that has four right anglecorners.

3. STARS Melinda wants to know theangle of elevation of a star above thehorizon. Based on the figure, what is theangle of elevation? Is this angle anacute, right, or obtuse angle?

4. CAKE Nick has a slice of cake. Hewants to cut it in half, bisecting the 46°angle formed by the straight edges ofthe slice. What will be the measure ofthe angle of each of the resulting pieces?

ROADS For Exercises 5–7, use thefollowing figure.

5. Central Street runs north-south andSpring Street runs east-west. What kindof angle do Central Street and SpringStreet make?

6. Valerie is driving down Spring Streetheading east. She takes a left onto RiverStreet. What type of angle did she haveto turn her car through?

7. What is the angle measure Valerie isturning her car when she takes the leftturn?

(x � 8)̊ (3x � 12)̊

Central St.

Spring St.

River St.

90

0 180

10

170

20

160

30150

40140

50

13060

12070

11080

100

100

80

110

70

12060

13050

140

4015

03016

02017

010

1800

O

Less

on

1-4

05-56 Geo-01-873958 4/3/06 6:29 PM Page 33

Page 5: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 40 Glencoe Geometry

Word Problem PracticeAngle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-5

1. LETTERS A sign painter is painting alarge “X”. What are the measures ofangles 1, 2, and 3?

2. PAPER Matthew cuts a straight linesegment through a rectangular sheet ofpaper. His cuts goes right through acorner. How are the two angles formedat that corner related?

3. PIZZA Ralph has sliced a pizza usingstraight line cuts through the center ofthe pizza. The slices are not exactly thesame size. Ralph notices that twoadjacent slices are complementary. If oneof the slices has a measure of 2xº, andthe other a measure of 3xº, what is themeasure of each angle?

4. GLASS Carlo dropped a piece of stainedglass and the glass shattered. He pickedup the piece shown on the left.

He wanted to find the piece that wasadjoining on the right. What should themeasurement of the angle marked witha question mark be? How is that anglerelated to the angle marked 106°?

LAYOUTS For Exercises 5–7, use thefollowing information.A rectangular plaza has a walking pathalong its perimeter in addition to two pathsthat cut across the plaza as shown in thefigure.

5. Find the measure of angle 1.

6. Find the measure of angle 4.

7. Name a pair of vertical angle in thefigure. What is the measure of �2?

12 3

4

135˚

50˚

Part of edge Missing Piece

106˚ ?

Cut1

2

120˚1

2

3

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-56 Geo-01-873958 4/3/06 6:29 PM Page 40

Page 6: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 47 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeTwo-Dimensional Figures

NAME ______________________________________________ DATE ____________ PERIOD _____

1-6

1. ARCHITECTURE In the Uffizi gallery inFlorence, Italy, there is a room filledwith paintings by Bronzino called theTribune room (La Tribuna in Italian).The floor plan of the room is shownbelow.

What kind of polygon is the floor plan?

2. JOGGING Vassia decides to jog arounda city park. The park is shaped like acircle with a diameter of 300 yards. IfVassia makes one loop around the park,approximately how far has she run?

3. PORTRAITS Around 1550, AgnoloBronzino painted a portrait of Eleonoreof Toledo and her son. The paintingmeasures 115 centimeters by 96centimeters. What is the area of thepainting?

4. ORIGAMI Jane takes a square piece ofpaper and folds it in half making acrease that connects the midpoints oftwo opposite sides. The original piece ofpaper was 8 inches on a side. What isthe perimeter of the resulting rectangle?

STICKS For Exercises 5–7, use thefollowing information.Amy has a box of teriyaki sticks. They areall 15 inches long. She creates rectanglesusing the sticks by placing them end to endlike the rectangle shown in the figure.

5. How many different rectangles can shemake that use exactly 12 of the sticks?What are their dimensions?

6. What is the perimeter of each rectanglelisted in Exercise 5?

7. Which of the rectangles in Exercise 5has the largest area?

300 yards

La Tribuna

Less

on

1-6

05-56 Geo-01-873958 4/3/06 6:29 PM Page 47

Page 7: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 1 54 Glencoe Geometry

Word Problem PracticeThree-Dimensional Figures

NAME ______________________________________________ DATE ____________ PERIOD _____

1-7

1. KEPLER For some time, JohannesKepler thought that the Platonic solidswere related to the orbits of the planets.He made models of each of the Platonicsolids. He made a frame of each of theplatonic solids by fashioning togetherwooden edges. How many wooden edgesdid Kepler have to make for the cube?

2. OCTAGONAL BUILDINGS ThomasJefferson built an octagonal building in1805 in Virginia. In fact, the building isroughly shaped like a regular octagonalprism. Complete the following table.

3. TRASH CANS A cylindrical trash can is 30 inches high and has a base radiusof 7 inches. What is the outside surfacearea of this trash can, including the topof the lid? Round your answer to thenearest square inch.

4. ALGAE Ronald owns a fish tank in theshape of a rectangular box. The tank is18 inches high, 14 inches deep, and 30inches long. Ronald went on a one-monthvacation. When he returned he foundthat the sides and bottom of his fishtank were covered with algae. What isthe area that was covered?

SILOS For Exercises 5–7, use thefollowing information.A silo is shaped like a cylinder with a coneon top. The radii of the bases of the cylinderand cone are both equal to 8 feet. Theheight of the cylindrical part is 25 feet andthe height of the cone is 6 feet.

5. What is the volume of the cylindricalpart of the silo? Round your answer tothe nearest cubic foot.

6. What is the volume of the conical part ofthe silo? Round your answer to thenearest cubic foot.

7. What is the volume of the entire silo?Round your answer to the nearest cubicfoot.

7 in.

30 in.

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

Attributes of a Regular Octagonal Prism

No. of Vertices

No. of Edges

No. of Faces

05-56 Geo-01-873958 4/3/06 6:29 PM Page 54

Page 8: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

1. RAMPS Rodney is rolling marbles downa ramp. Every second that passes, hemeasures how far the marbles travel. Herecords the information in the tableshown below.

Make a conjecture about how far themarble will roll in the fifth second.

2. PRIMES A prime number is a numberother than 1 that is divisible by onlyitself and 1. Lucille read that primenumbers are very important incryptography, so she decided to find asystematic way of producing primenumbers. After some experimenting,she conjectured that 2n � 1 is a primefor all whole numbers n � 1. Find acounterexample to this conjecture.

3. GENEOLOGY Miranda is developing a chart that shows her ancestry. Shemakes the three sketches shown below.The first dot represents herself. Thesecond sketch represents herself and her parents. The third sketch represents herself, her parents, and her grandparents.

Sketch what you think would be thenext figure in the sequence.

4. MEDALS Barbara is in charge of theaward medals for a sporting event. Shehas 31 medals to give out to variousindividuals on 6 competing teams. Sheasserts that at least one team will endup with more than 5 medals. Do youbelieve her assertion? If you do, try toexplain why you think her assertion istrue, and if you do not, explain how shecan be wrong.

PATTERNS For Exercises 5–7, use thefollowing information.The figure shows a sequence of squareseach made out of identical square tiles.

5. Starting from zero tiles, how many tilesdo you need to make the first square?How many tiles do you have to add to the first square to get the secondsquare? How many tiles do you have to add to the second square to get thethird square?

6. Make a conjecture about the list ofnumbers you started writing in youranswer to Exercise 5.

7. Make a conjecture about the sum of thefirst n odd numbers.

Chapter 2 10 Glencoe Geometry

Word Problem PracticeInductive Reasoning and Conjecture

NAME ______________________________________________ DATE ____________ PERIOD _____

2-1C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

Second 1st 2nd 3rd 4th

Distance (cm) 20 60 100 140

05-62 Geo-02-873959 4/4/06 11:30 AM Page 10

Page 9: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 18 Glencoe Geometry

Word Problem PracticeLogic

NAME ______________________________________________ DATE ____________ PERIOD _____

2-2C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. HOCKEY Carol asked John if hishockey team won the game last nightand if he scored a goal. John said “yes.”Carol then asked Peter if he or Johnscored a goal at the game. Peter said“yes.” What can you conclude aboutwhether or not Peter scored?

2. CHOCOLATE Nash has a bag ofminiature chocolate bars that come intwo distinct types: dark and milk.Nash picks a chocolate out of the bag.Consider these statements:p: the chocolate bar is dark chocolateq: the chocolate bar is milk chocolateIs the following statement true?

�(�p � �q)

3. VIDEO GAMES Harold is allowed toplay video games only if he washes thedishes or takes out the trash. However,if Harold does not do his homework, heis not allowed to play video games underany circumstance. Complete the truthtable.p: Harold has washed the dishesq: Harold has taken out the trashr: Harold has done his homeworks: Harold is allowed to play video games

4. CIRCUITS In Earl’s house, the diningroom light is controlled by two switchesaccording to the following table.

If up and on are considered true anddown and off are considered false, writean expression that gives the truth valueof the light as a function of the truthvalues of the two switches.

READING For Exercises 5–7, use thefollowing information.Two hundred people were asked what kindof literature they like to read. They couldchoose among novels, poetry, and plays. Theresults are shown in the Venn diagram.

5. How many people said they like allthree types of literature?

6. How many like to read poetry?

7. What percentage of the people who likeplays also like novels and poetry?

Novels45

Poetry6

Plays26

572

38

8

p q r s

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Switch A Switch B Light

up up off

up down on

down up on

down down off

05-62 Geo-02-873959 4/4/06 11:30 AM Page 18

Page 10: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 26 Glencoe Geometry

Word Problem PracticeConditional Statements

NAME ______________________________________________ DATE ____________ PERIOD _____

2-3C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. TANNING Maya reads in a paper thatpeople who tan themselves under the Sun for extended periods are atincreased risk of skin cancer. From thisinformation, can she conclude that shewill not increase her risk of skin cancerif she avoids tanning for extendedperiods of time?

2. PARALLELOGRAMS Clark says thatbeing a parallelogram is equivalent to being a quadrilateral with equalopposite angles. Write his statement in if-then form.

3. AIR TRAVEL Ulma is waiting to boardan airplane. Over the speakers shehears a flight attendant say “If you areseated in rows 10 to 20, you may nowboard.” What are the inverse, converse,and the contrapositive of this statement?

4. MEDICATION Linda’s medicine bottlesays “If you are pregnant, then youcannot take this medicine.” What are theinverse, converse, and the contrapositiveof this statement?

VENN DIAGRAMS For Exercises 5–8,use the following information.Jose made this Venn diagram to show howrectangles, squares, and rhombi are related.(A rhombus is a quadrilateral with foursides of equal length.)

Let Q be a quadrilateral. For each problemtell whether the statement is true or false.If it is false, provide a counterexample.

5. If Q is a square, then Q a rectangle.

6. If Q is not a rectangle, then Q is not arhombus.

7. If Q is a rectangle but not a square,then Q is not a rhombus.

8. If Q is not a rhombus, then Q is not asquare.

Rectangles

Squ

ares

Rhombi

05-62 Geo-02-873959 4/4/06 11:31 AM Page 26

Page 11: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 33 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeDeductive Reasoning

NAME ______________________________________________ DATE ____________ PERIOD _____

2-4

Less

on

2-4

1. SIGNS Two signs are posted on ahaunted house.

Inside the haunted house, you find achild with his parent. What can youdeduce about the age of the child basedon the house rules?

2. LOGIC As Laura’s mother rushed off to work, she quickly gave Laura someinstructions. “If you need me, try my cell . . . if I don’t answer it means I’m ina meeting, but don’t worry, the meetingwon’t last more than 30 minutes and I’ll call you back when it’s over.” Laterthat day, Laura needed her mother, buther mother was stuck in a meeting and couldn’t answer the phone. Lauraconcludes that she will have to wait nomore than 30 minutes before she gets a call back from her mother. What law of logic did Laura use to draw thisconclusion?

3. MUSIC Composer Ludwig vanBeethoven wrote 9 symphonies and 5piano concertos. If you lived in Vienna in the early 1800s, you could attend aconcert conducted by Beethoven himself.Write a valid conclusion to thehypothesis If Mozart could not attend aconcert conducted by Beethoven, . . .

4. DIRECTIONS Hank has anappointment to see a financial advisoron the fifteenth floor of an officebuilding. When he gets to the building,the people at the front desk tell him that if he wants to go to the fifteenthfloor, then he must take the red elevator.While looking for the red elevator, aguard informs him that if he wants tofind the red elevator he must find thereplica of Michelangelo’s David. When he finally got to the fifteenth floor, hisfinancial advisor greeted him asking,“What did you think of theMichelangelo?” How did Hank’s financialadvisor conclude that Hank must haveseen the Michelangelo statue?

LAWS For Exercises 5 and 6, use thefollowing information.The law says that if you are under 21,then you are not allowed to drink alcoholicbeverages and if you are under 18, then you are not allowed to vote. For eachproblem give the possible ages of the person described or state that the personcannot exist.

5. John cannot drink wine legally but isallowed to vote.

6. Mary cannot vote legally but can drinkbeer legally.

NO ONEUNDER

5ALLOWED

NO ONEUNDER 8ALLOWED

WITHOUT APARENT

05-62 Geo-02-873959 4/4/06 11:31 AM Page 33

Page 12: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 40 Glencoe Geometry

Word Problem PracticePostulates and Paragraph Proofs

NAME ______________________________________________ DATE ____________ PERIOD _____

2-5C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. ROOFING Noel and Kirk are building anew roof. They wanted a roof with twosloping planes that meet along a curvedarch. Is this possible?

2. AIRLINES An airline company wants toprovide service to San Francisco, LosAngeles, Chicago, Dallas, Washington D. C., and New York City. The companyCEO draws lines between each pair ofcities in the list on a map. No three ofthe cities are collinear. How many linesdid the CEO draw?

3. TRIANGULATION A sailor spots awhale through her binoculars. Shewonders how far away the whale is, butthe whale does not show up on the radarsystem. She sees another boat in thedistance and radios the captain askinghim to spot the whale and record itsdirection. Explain how this addedinformation could enable the sailor topinpoint the location of the whale.Under what circumstance would thisidea fail?

4. POINTS Carson claims that a line canintersect a plane at only one point anddraws this picture to show hisreasoning.

Zoe thinks it is possible for a line tointersect a plane at more than one point.Who is correct? Explain.

FRIENDSHIPS For Exercises 5 and 6,use the following information.A small company has 16 employees. Theowner of the company became concernedthat the employees did not know each othervery well. He decided to make a picture ofthe friendships in the company. He placed16 points on a sheet of paper in such a way that no 3 were collinear. Each pointrepresented a different employee. He thenasked each employee who their friends were and connected two points with a linesegment if they represented friends.

5. What is the maximum number of linesegments that can be drawn betweenpairs among the 16 points?

6. When the owner finished the picture, hefound that his company was split intotwo groups, one with 10 people and theother with 6. The people within a groupwere all friends, but nobody from onegroup was a friend of anybody from theother group. How many line segmentswere there?

P

05-62 Geo-02-873959 4/4/06 11:31 AM Page 40

Page 13: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 47 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeAlgebraic Proof

NAME ______________________________________________ DATE ____________ PERIOD _____

2-6

Less

on

2-6

1. DOGS Jessica and Robert each own thesame number of dogs. Robert and Gailalso own the same number of dogs.Without knowing how many dogs theyown, one can still conclude that Jessicaand Gail each own the same number ofdogs. What property is used to make this conclusion?

2. MONEY Lars and Peter both have thesame amount of money in their wallets.They went to the store together anddecided to buy some cookies, splittingthe cost equally. After buying thecookies, do they still have the sameamount of money in their wallets? Whatproperty is relevant to help you decide?

4. MANUFACTURING A companymanufactures small electroniccomponents called diodes. Each diode is worth $1.50. Plant A produced 4,443diodes and Plant B produced 5,557diodes. The foreman was asked what the total value of all the diodes was.The foreman immediately responded“$15,000.” The foreman would not havebeen able to compute the value soquickly if he had to multiply $1.50 by4,443 and then add this to the result of $1.50 times 5,557. Explain how youthink the foreman got the answer soquickly?

4. FIGURINES Pete and Rhonda paintfigurines. They can both paint 8figurines per hour. One day, Pete worked6 hours while Rhonda worked 9 hours.How many figurines did they paint thatday? Show how to get the answer usingthe Distributive Property.

AGE For Exercises 5 and 6, use thefollowing information.William’s father is eight years older than 4 times William’s age. William’s father is 36 years old.

5. Let x be William’s age. Translate thegiven information into an algebraicequation involving x.

6. Fill in the missing steps andjustifications for each step in finding the value of x.

Algebraic Steps Properties

4x � 8 � 36 Original equation

Subtraction Property

4x � 28

�44x� � �

248�

Substitution Property

Page 14: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 54 Glencoe Geometry

Word Problem PracticeProving Segment Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

2-7C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. FAMILY Maria is 11 inches shorterthan her sister Nancy. Brad is 11 inchesshorter than his brother Chad. If Mariais shorter than Brad, how do the heightsof Nancy and Chad compare? What ifMaria and Brad are the same height?

2. DISTANCE Martha and Laura live1,400 meters apart. A library is openedbetween them and is 500 meters fromMartha.

How far is the library from Laura?

3. LUMBER Byron works in a lumberyard. His boss just cut a dozen planksand asked Byron to double check thatthey are all the same length. The plankswere numbered 1 through 12. Byrontook out plank number 1 and checkedthat the other planks are all the samelength as plank 1. He concluded thatthey must all be the same length.Explain how you know plank 7 andplank 10 are the same length eventhough they were never directlycompared to each other?

4. NEIGHBORHOODS Karla, John, andMandy live in three houses that are onthe same line. John lives between Karlaand Mandy. Karla and Mandy live a mileapart. Is it possible for John to be a milefrom both Karla and Mandy?

LIGHTS For Exercises 5 and 6, use thefollowing information.Five lights, A, B, C, D, and E, are lined upin a row. The middle light is the midpoint of the second and fourth light and also themidpoint of the first and last light.

5. Draw a figure to illustrate the situation.

6. Complete this proof.

Given: C is the midpoint of B�D� and A�E�.Prove: AB � DE

Statement Reason1. C is the midpoint 1. Given

of B�D� and A�E�.2. BC � CD and 2.

3. AC � AB � BC, 3.CE � CD � DE

4. AB � AC � BC 4.

5. 5. Substitution Property

6. DE � CE � CD 6.

7. 7.

Martha Library Laura

500 meters

1400 meters

05-62 Geo-02-873959 4/4/06 11:31 AM Page 54

Page 15: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 2 61 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeProving Angle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

2-8

Less

on

2-8

1. ICOSAHEDRA For a school project,students are making a gianticosahedron, which is a large solid withmany identical triangular faces. John isassigned quality control. He must makesure that the measures of all the anglesin all the triangles are the same as eachother. He does this by using a precuttemplate and comparing the cornerangles of every triangle to the template.How does this assure that the angles inall the triangles will be congruent toeach other?

2. VISTAS If you look straight ahead at ascenic point, you can see a waterfall. Ifyou turn your head 25º to the left, youwill see a famous mountain peak. If youturn your head 35º more to the left, youwill see another waterfall. If you arelooking straight ahead, through howmany degrees must you turn your headto the left in order to see the secondwaterfall?

3. TUBES A tube with a hexagonal crosssection is placed on the floor.

What is the measure of �1 in the figuregiven that the angle at one corner of thehexagon is 120°?

4. PAINTING Students are painting theirrectangular classroom ceiling. They wantto paint a line that intersects one of thecorners as shown in the figure.

They want the painted line to make a15° angle with one edge of the ceiling.Unfortunately, between the line and theedge there is a water pipe making itdifficult to measure the angle. Theydecide to measure the angle to the otheredge. Given that the corner is a rightangle, what is the measure of the otherangle?

For Exercises 5–7, use the followinginformation.Clyde looks at a building from point E.�AEC has the same measure as �BED.

5. The measure of �AEC is equal to thesum of the measures of �AEB and whatother angle?

6. The measure of �BED is equal to thesum of the measures of �CED and whatother angle?

7. Is it true that m�AEB is equal tom�CED?

E

A

B

C

D

Cross section of pipe

15˚

120˚ 1

05-62 Geo-02-873959 4/4/06 11:31 AM Page 61

Page 16: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 10 Glencoe Geometry

Word Problem PracticeParallel Lines and Transversals

NAME ______________________________________________ DATE ____________ PERIOD _____

3-1

1. FIGHTERS Two fighter aircraft fly at the same speed and in the samedirection leaving a trail behind them.Describe the relationship between thesetwo trails.

2. ESCALATORS An escalator at ashopping mall runs up several levels.The escalator railing can be modeled bya straight line running past horizontallines that represent the floors.

Describe the relationships of these lines.

3. DESIGN Carol designed the pictureframe shown below. How many pairs of parallel segments are there amongvarious edges of the frame?

4. NEIGHBORHOODS John, Georgia, andPhillip live nearby each other as shownin the map.

Describe how their corner angles relate to each other in terms of alternate interior, alternate exterior,corresponding, consecutive interior, orvertical angles.

MAPPING For Exercises 5 and 6, usethe following figure.

5. Connor lives at the angle that forms analternate interior angle with Georgia’sresidence. Add Connor to the map.

6. Quincy lives at the angle that forms aconsecutive interior angle with Connors’residence. Add Quincy to the map.

High Street

Bay Stre

et

Low Street

GeorgiaJohn

Phillip

High Street

Bay Stre

et

Low Street

GeorgiaJohn

Phillip

Floor A

Floor B

Escalator Railing

Floor C

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-48 Geo-03-873960 3/30/06 2:09 PM Page 10

Page 17: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 17 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeAngles and Parallel Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

3-2

Less

on

3-2

1. RAMPS A parking garage ramp rises to connect two horizontal levels of aparking lot. The ramp makes a 10°angle with the horizontal. What is themeasure of angle 1 in the figure?

2. BRIDGES A double decker bridge hastwo parallel levels connected by anetwork of diagonal girders. One of thegirders makes a 52° angle with thelower level as shown in the figure. Whatis the measure of angle 1?

3. CITY ENGINEERING Seventh Avenueruns perpendicular to both 1st and 2ndStreets, which are parallel. However,Maple Avenue makes a 115° angle with2nd Street. What is the measure of angle 1?

4. PODIUMS A carpenter is building apodium. The side panel of the podium iscut from a rectangular piece of wood.

The rectangle must be sawed along thedashed line in the figure. What is themeasure of angle 1?

SECURITY For Exercises 5 and 6, usethe following information.An important bridge crosses a river at a keylocation. Because it is so important, roboticsecurity cameras are placed at the locationsof the dots in the figure. Each robot canscan x degrees. On the lower bank, it takes4 robots to cover the full angle from theedge of the river to the bridge. On the upperbank, it takes 5 robots to cover the fullangle from the edge of the river to thebridge.

5. How are the angles that are covered by the robots at the lower and upperbanks related? Derive an equation that x satisfies based on this relationship.

6. How wide is the scanning angle for eachrobot? What are the angles that thebridge makes with the upper and lowerbanks?

upper bank

lower bank

Brid

ge

116˚

1

Map

le Av

e.

115˚

1

2nd St.

1st St.

7th

Ave.

52˚

1

RampLevel 2

Level 110˚1

05-48 Geo-03-873960 3/30/06 2:09 PM Page 17

Page 18: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 24 Glencoe Geometry

Word Problem PracticeSlopes of Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

3-3C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. HIGHWAYS A highway on-ramp rises15 feet for every 100 horizontal feettraveled. What is the slope of the ramp?

2. DESCENT An airplane descends at arate of 300 feet for every 5000 horizontalfeet that the plane travels. What is theslope of the path of descent?

3. ROAD TRIP Jenna is driving 400 milesto visit her grandmother. She managesto travel the first 100 miles of her trip intwo hours. If she continues at this rate,how long will it take her to drive theremaining distance?

4. WATER LEVEL Before the rain began,the water in a lake was 268 inches deep.The rain began and after four hours ofrain, the lake was 274 inches deep. Therain continued for one more hour at thesame intensity. What was the depth ofthe lake when the rain stopped?

CITY BLOCKS For Exercises 5–8, usethe following information.The figure shows a map of part of a cityconsisting of two pairs of parallel roads. If acoordinate grid is applied to this map, FordStreet would have a slope of �3.

5. The intersection of B Street and Ford Street is 150 yards east of theintersection of Ford Street and CloverStreet. How many yards south is it?

6. What is the slope of 6th Street? Explain.

7. What are the slopes of Clover and BStreets? Explain.

8. The intersection of B Street and 6th Street is 600 yards east of theintersection of B Street and Ford Street.How many yards north is it?

Clover St.

6th St.Ford St.

B St.

N

05-48 Geo-03-873960 3/30/06 2:09 PM Page 24

Page 19: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 32 Glencoe Geometry

Word Problem PracticeEquations of Lines

NAME ______________________________________________ DATE ____________ PERIOD _____

3-4C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. GROWTH At the same time eachmonth over a one year period, Johnrecorded the height of a tree he hadplanted. He then calculated the averagegrowth rate of the tree. The height h ininches of the tree during this period was given by the formula h � 1.7t � 28,where t is the number of months. Whatare the slope and y-intercept of this lineand what do they signify?

2. DRIVING Ellen is driving to a friend’shouse. The graph shows the distance (in miles) that Ellen was from home tminutes after she left her house.

Write an equation that relates m and t.

3. COST Carla has a business that teststhe air quality in artist’s studios. Shehad to purchase $750 worth of testingequipment to start her business. Shecharges $50 to perform the test. Let n bethe number of jobs she gets and let P beher net profit. Write an equation thatrelates P and n. How many jobs does sheneed to make $750?

4. PAINT TESTING A paint companydecided to test the durability of its whitepaint. They painted a square all whitewith their paint and measured thereflectivity of the square each year.Seven years after being painted, thereflectivity was 85%. Ten years afterbeing painted, the reflectivity dropped to 82.9%. Assuming that the reflectivitydecreases steadily with time, write anequation that gives the reflectivity R (asa percentage) as a function of time t inyears. What is the reflectivity of a freshcoat of their white paint?

ARTISTRY For Exercises 5–7, use thefollowing information.Gail is an oil painter. She paints oncanvases made from Belgian linen. Beforeshe paints on the linen, she has to primethe surface so that it does not absorb the oilfrom the paint she uses. She can buy linenthat has already been primed for $21 peryard, or she can buy unprimed linen for $15per yard, but then she would also have tobuy a jar of primer for $30.

5. Let P be the cost of Y yards of primedBelgian linen. Write an equation thatrelates P and Y.

6. Let U be the cost of buying Y yards ofunprimed linen and a jar of primer.Write an equation that relates U and Y.

7. For how many yards would it be lessexpensive for Gail to buy the primedlinen?

m

tO 5

5

05-48 Geo-03-873960 3/30/06 2:09 PM Page 32

Page 20: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 39 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeProving Lines Parallel

NAME ______________________________________________ DATE ____________ PERIOD _____

3-5

Less

on

3-5

1. RECTANGLES Jim made a frame for a painting. He wants to check to makesure that opposite sides are parallel bymeasuring the angles at the corners andseeing if they are right angles. Howmany corners must he check in order tobe sure that the opposite sides areparallel?

2. BOOKS The two gray books on thebookshelf each make a 70° angle withthe base of the shelf.

What more can you say about these twogray books?

3. PATTERNS A rectangle is cut along theslanted, dashed line shown in the figure.The two pieces are rearranged to formanother figure. Describe as precisely asyou can the shape of the new figure.Explain.

4. FIREWORKS A fireworks display isbeing readied for a celebration. Thedesigners want to have four fireworksshoot out along parallel trajectories.They decide to place two launchers on adock and the other two on the roof of abuilding.

To pull off this display, what should themeasure of angle 1 be?

SIGNS For Exercises 5 and 6, use thefollowing information.Harold is making a giant letter “A” to put onthe rooftop of the “A is for Apple” OrchardStore. The figure shows a sketch of thedesign

5. What should the measures of angles 1and 2 be so that the horizontal part ofthe “A” is truly horizontal?

6. When building the “A,” Harold makessure that angle 1 is correct, but when hemeasures angle 2, it is not correct. Whatdoes this imply about the “A”?

21 108˚

70˚

30˚

1

05-48 Geo-03-873960 3/30/06 2:09 PM Page 39

Page 21: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 3 46 Glencoe Geometry

Word Problem PracticePerpendiculars and Distance

NAME ______________________________________________ DATE ____________ PERIOD _____

3-6C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. DISTANCE What does it mean if thedistance between a point P and a line l is zero? What does it mean if thedistance between two lines is zero?

2. DISTANCE Paul is standing in theschoolyard. The figure shows hisdistance from various classroom doorslined up along the same wall.

How far is Paul from the wall itself?

3. SEASHELLS Mason is standing on theseashore. He believes that if he makes awish and throws a seashell back into theocean, his wish will come true. Mason isstanding at the origin of a coordinateplane and the shoreline is representedby the graph of the line y � 1.5 x � 13.Each unit represents 1 meter. How fardoes Mason need to be able to throw theseashell to throw one into the ocean?Round your answer to the nearestcentimeter.

4. SUPPORTS Two support beams aremodeled by the lines y � 2x � 10 and y � 2x � 15. What is the distancebetween these two lines?

RESCUE For Exercises 5–7, use thefollowing information.Rachel sees a baseball heading straight forher friend Brad. Brad has no idea that he isabout to be hit by a baseball.

Rachel decides to run and intercept thebaseball. Rachel is located at (�3, 7). Bradis at (�1, �6.25). The baseball is currentlyat (20, 2.5) and closing fast.

5. What is the equation of the line thatpasses through Brad and the baseball?

6. If Rachel runs along the path of shortestdistance to intercept (i.e. along the lineperpendicular to the trajectory of thebaseball), what are the coordinates ofthe point where she will end up whenshe is between Brad and the baseball?

7. What is the shortest distance thatRachel must run in order to get betweenher friend and the baseball?

y

xO

5

5 10 15 20

-5

Rachel

Brad

Baseball

295 ft246 ft

283 ft

396 ft

Paul

05-48 Geo-03-873960 3/30/06 2:09 PM Page 46

Page 22: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 10 Glencoe Geometry

Word Problem PracticeClassifying Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

4-1

1. MUSEUMS Paul is standing in front ofa museum exhibition. When he turns hishead 60° to the left, he can see a statueby Donatello. When he turns his head60° to the right, he can see a statue byDella Robbia. The two statues and Paulform the vertices of a triangle. Classifythis triangle as acute, right, or obtuse.

2. PAPER Marsha cuts a rectangular pieceof paper in half along a diagonal. Theresult is two triangles. Classify thesetriangles as acute, right, or obtuse.

3. WATERSKIING Kim and Cassandra are waterskiing. They are holding on toropes that are the same length and tiedto the same point on the back of a speedboat. The boat is going full speed aheadand the ropes are fully taut.

Kim, Cassandra, and the point wherethe ropes are tied on the boat form thevertices of a triangle. The distancebetween Kim and Cassandra is neverequal to the length of the ropes. Classifythe triangle as equilateral, isosceles, orscalene.

4. BOOKENDS Two bookends are shapedlike right triangles.

The bottom side of each triangle isexactly half as long as the slanted sideof the triangle. If all the books betweenthe bookends are removed and they arepushed together, they will form a singletriangle. Classify the triangle that canbe formed as equilateral, isosceles, orscalene.

DESIGNS For Exercises 5 and 6, use thefollowing information.Suzanne saw this pattern on a pentagonalfloor tile. She noticed many different kindsof triangles were created by the lines on thetile.

5. Identify five triangles that appear to beacute isosceles triangles.

6. Identify five triangles that appear to beobtuse isosceles triangles.

CAG H

IFJ

B

E DKim

Cassandra

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-56 Geo-04-873961 4/3/06 4:53 PM Page 10

Page 23: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 17 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeAngles of Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

4-2

Less

on

4-2

1. PATHS Eric walks around a triangularpath. At each corner, he records themeasure of the angle he creates.

He makes one complete circuit aroundthe path. What is the sum of the three angle measures that he wrotedown?

2. STANDING Sam, Kendra, and Tony arestanding in such a way that if lines weredrawn to connect the friends they wouldform a triangle.

If Sam is looking at Kendra he needs toturn his head 40º to look at Tony. If Tonyis looking at Sam he needs to turn hishead 50º to look at Kendra. How manydegrees would Kendra have to turn herhead to look at Tony if she is looking atSam?

3. TOWERS A lookout tower sits on anetwork of struts and posts. Lesliemeasured 2 angles on the tower.

What is the measure of angle 1?

4. ZOOS The zoo lights up thechimpanzee pen with an overhead lightat night. The cross section of the lightbeam makes an isosceles triangle.

The top angle of the triangle is 52° andthe exterior angle is 116º. What is themeasure of angle 1?

DRAFTING For Exercises 5 and 6, usethe following information.Chloe bought a drafting table and set it upso that she can draw comfortably from herstool. Chloe measured the two anglescreated by the legs and the tabletop in caseshe had to dismantle the table.

5. Which of the four numbered angles canChloe determine by knowing the twoangles formed with the tabletop? Whatare their measures?

6. What conclusion can Chloe make aboutthe unknown angles before shemeasures them to find their exactmeasurements?

29˚68˚

12

3 4

52˚

116˚1

62˚136˚

Kendra

Tony

Sam

Page 24: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 26 Glencoe Geometry

Word Problem PracticeCongruent Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

4-3C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. PICTURE HANGING Candice hung apicture that was in a triangular frameon her bedroom wall.

One day, it fell to the floor, but did notbreak or bend. The figure shows theobject before and after the fall. Label the vertices on the frame after the fallaccording to the “before” frame.

2. SIERPINSKI’S TRIANGLE The figurebelow is a portion of Sierpinski’sTriangle. The triangle has the propertythat any triangle made from anycombination of edges is equilateral.How many triangles in this portion arecongruent to the black triangle at thebottom corner?

3. QUILTING Stefan drew this pattern fora piece of his quilt. It is made up ofcongruent isosceles right triangles. Hedrew one triangle and then repeatedlydrew it all the way around.

What are the missing measures of theangles of the triangle?

4. MODELS Dana bought a modelairplane kit. When he opened the box,these two congruent triangular pieces of wood fell out of it.

Identify the triangle that is congruent to�ABC.

GEOGRAPHY For Exercises 5 and 6,use the following information.Igor noticed on a map that the trianglewhose vertices are the supermarket, thelibrary, and the post office (�SLP) iscongruent to the triangle whose vertices areIgor’s home, Jacob’s home, and Ben’s home(�IJB). That is, �SLP � �IJB.

5. The distance between the supermarketand the post office is 1 mile. Which pathalong the triangle �IJB is congruent tothis?

6. The measure of �LPS is 40. Identify theangle that is congruent to this angle in�IJB.

A

B

CQ

R

P

45˚

Before

A B

C

After

05-56 Geo-04-873961 4/3/06 4:54 PM Page 26

Page 25: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 33 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeProving Congruence—SSS, SAS

NAME ______________________________________________ DATE ____________ PERIOD _____

4-4

Less

on

4-4

1. STICKS Tyson had three sticks oflengths 24 inches, 28 inches, and 30inches. Is it possible to make twononcongruent triangles using the samethree sticks? Explain.

2. BAKERY Sonia made a sheet ofbaklava. She has markings on her panso that she can cut them into largesquares. After she cuts the pastry insquares, she cuts them diagonally toform two congruent triangles. Whichpostulate could you use to prove the two triangles congruent?

3. CAKE Carl had a piece of cake in theshape of an isosceles triangle withangles 26°, 77°, and 77°. He wanted todivide it into two equal parts, so he cutit through the middle of the 26° angle tothe midpoint of the opposite side. Hesays that because he is dividing it at themidpoint of a side, the two pieces arecongruent. Is this enough information?Explain.

4. TILES Tammy installs bathroom tiles.Her current job requires tiles that areequilateral triangles and all the tileshave to be congruent to each other. Shehas a big sack of tiles all in the shape of equilateral triangles. Although sheknows that all the tiles are equilateral,she is not sure they are all the samesize. What must she measure on eachtile to be sure they are congruent?Explain.

INVESTIGATION For Exercises 5 and 6,use the following information.An investigator at a crime scene found atriangular piece of torn fabric. Theinvestigator remembered that one of thesuspects had a triangular hole in their coat.Perhaps it was a match. Unfortunately, toavoid tampering with evidence, theinvestigator did not want to touch the fabricand could not fit it to the coat directly.

5. If the investigator measures all threeside lengths of the fabric and the hole,can the investigator make a conclusionabout whether or not the hole could have been filled by the fabric?

6. If the investigator measures two sides of the fabric and the included angle andthen measures two sides of the hole andthe included angle can he determine if itis a match? Explain.

05-56 Geo-04-873961 4/3/06 4:54 PM Page 33

Page 26: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 40 Glencoe Geometry

Word Problem PracticeProving Congruence—ASA, AAS

NAME ______________________________________________ DATE ____________ PERIOD _____

4-5C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. DOOR STOPS Two door stops havecross-sections that are right triangles.They both have a 20° angle and thelength of the side between the 90° and20° angles are equal. Are the cross-sections congruent? Explain.

2. MAPPING Two people decide to take awalk. One person is in Bombay and theother is in Milwaukee. They start bywalking straight for 1 kilometer. Thenthey both turn right at an angle of 110°,and continue to walk straight again.After a while, they both turn rightagain, but this time at an angle of 120°.They each walk straight for a while inthis new direction until they end upwhere they started. Each person walkedin a triangular path at their location.Are these two triangles congruent?Explain.

3. CONSTRUCTION The rooftop ofAngelo’s house creates an equilateraltriangle with the attic floor. Angelowants to divide his attic into 2 equalparts. He thinks he should divide it byplacing a wall from the center of the roofto the floor at a 90° angle. If Angelo doesthis, then each section will share a sideand have corresponding 90° angles.What else must be explained to provethat the two triangular sections arecongruent?

3. LOGIC When Carolyn finished hermusical triangle class, her teacher gaveeach student in the class a certificate inthe shape of a golden triangle. Eachstudent received a different shapedtriangle. Carolyn lost her triangle on herway home. Later she saw part of agolden triangle under a grate.

Is enough of the triangle visible to allowCarolyn determine that the triangle isindeed hers? Explain.

PARK MAINTENANCE For Exercises 5and 6, use the following information.Park officials need a triangular tarp tocover a field shaped like an equilateraltriangle 200 feet on a side.

5. Suppose you know that a triangular tarphas two 60° angles and one side oflength 200 feet. Will this tarp cover thefield? Explain.

6. Suppose you know that a triangular tarphas three 60° angles. Will this tarpnecessarily cover the field? Explain.

90˚ 90˚

05-56 Geo-04-873961 4/3/06 4:54 PM Page 40

Page 27: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 47 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeIsosceles Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

4-6

Less

on

4-6

1. TRIANGLES At an art supply store, twodifferent triangular rulers are available.One has angles 45°, 45°, and 90°. Theother has angles 30°, 60°, and 90°.Which triangle is isosceles?

2. RULERS A foldable ruler has two hingesthat divide the ruler into thirds. If theends are folded up until they touch,what kind of triangle results?

3. HEXAGONS Juanita placed one end ofeach of 6 black sticks at a common pointand then spaced the other ends evenlyaround that point. She connected thefree ends of the sticks with lines. Theresult was a regular hexagon. Thisconstruction shows that a regularhexagon can be made from six congruenttriangles. Classify these triangles.Explain.

4. PATHS A marble path is constructedout of several congruent isoscelestriangles. The vertex angles are all 20°.What is the measure of angle 1 in thefigure?

BRIDGES For Exercises 5–7, use thefollowing information.Every day, cars drive through isoscelestriangles when they go over the LeonardZakim Bridge in Boston. The ten-laneroadway forms the bases of the triangles.

5. The angle labeled A in the picture has ameasure of 67°. What is the measure of�B?

6. What is the measure of �C?

7. Name the two congruent sides.

A

B

C

1

05-56 Geo-04-873961 4/3/06 4:54 PM Page 47

Page 28: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 4 54 Glencoe Geometry

Word Problem PracticeTriangles and Coordinate Proof

NAME ______________________________________________ DATE ____________ PERIOD _____

4-7C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. SHELVES Martha has a shelf bracketshaped like a right isosceles triangle.She wants to know the length of thehypotenuse relative to the sides. Shedoes not have a ruler, but remembersthe Distance Formula. She places thebracket on a coordinate grid with theright angle at the origin. The length ofeach leg is a. What are the coordinatesof the vertices making the two acuteangles?

2. FLAGS A flag is shaped like anisosceles triangle. A designer would liketo make a drawing of the flag on a coordinate plane. Shepositions it so that the base of the triangle is on the y-axiswith one endpoint located at(0, 0). She locates the tip of the flag at (a, �

b2�). What are

the coordinates of the thirdvertex?

3. BILLIARDS The figure shows asituation on a billiard table.

What are the coordinates of the cue ballbefore it is hit and the point where thecue ball hits the edge of the table?

4. TENTS The entrance to Matt’s tentmakes an isosceles triangle. If placed ona coordinate grid with the base on thex–axis and the left corner at the origin,the right corner would be at (6, 0) andthe vertex angle would be at (3, 4). Provethat it is an isosceles triangle.

DRAFTING For Exercises 5–7, use thefollowing information.An engineer is designing a roadway. Threeroads intersect to form a triangle. Theengineer marks two points of the triangle at (�5, 0) and (5, 0) on a coordinate plane.

5. Describe the set of points in thecoordinate plane that could not be usedas the third vertex of the triangle.

6. Describe the set of points in thecoordinate plane that would make thevertex of an isosceles triangle togetherwith the two congruent sides.

7. Describe the set of points in thecoordinate plane that would make aright triangle with the other two pointsif the right angle is located at (�5, 0).

(–b, ?) y

xO

(0, 0)

05-56 Geo-04-873961 4/3/06 4:54 PM Page 54

Page 29: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 5 10 Glencoe Geometry

Word Problem PracticeBisectors, Medians, and Altitudes

NAME ______________________________________________ DATE ____________ PERIOD _____

5-1C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. BALANCING Johanna balanced atriangle flat on her finger tip. Whatpoint of the triangle must Johanna betouching?

2. PICNICS Marsha and Bill are going to the park for a picnic. The park istriangular. One side of the park isbordered by a river and the other twosides are bordered by busy streets.Marsha and Bill want to find a spot thatis equally far away from the river andthe streets. At what point in the parkshould they set up their picnic?

3. MOVING Martin has 3 grown children.The figure shows the locations ofMartin’s children on a map that has acoordinate plane on it. Martin would liketo move to a location that is the samedistance from all three of his children.What are the coordinates of the locationon the map that is equidistant from allthree children?

4. NEIGHBORHOOD Amanda is lookingat her neighborhood map. She noticesthat her house along with the homes ofher friends Brian, and Cathy can be thevertices of a triangle. The map is on acoordinate grid. Amanda’s house is atthe point (1, 3) Brian’s is at (5, �1), andCathy’s is at (4, 5). Where would thethree friends meet if they each left theirhouses at the same time and walked tothe opposite side of the triangle alongthe path of shortest distance from theirhouse?

PLAZAS For Exercises 5–7, use thefollowing information.An architect is designing a triangular plaza.For aesthetic purposes, the architect paysspecial attention to the location of thecentroid C and the circumcenter O.

5. Give an example of a triangular plazawhere C � O. If no such example exists,state that this is impossible.

6. Give an example of a triangular plazawhere C is inside the plaza and O isoutside the plaza. If no such exampleexists, state that this is impossible.

7. Give an example of a triangular plazawhere C is outside the plaza and O isinside the plaza. If no such exampleexists, state that this is impossible.

y

xO

5

5-5

05-42 Geo-05-873962 4/3/06 4:57 PM Page 10

Page 30: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 5 17 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeInequalities and Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

5-2

Less

on

5-2

1. DISTANCE Carl and Rose live on thesame straight road. From their balconiesthey can see a flagpole in the distance.The angle that each person’s line ofsight to the flagpole makes with theroad is the same. How do their distancesfrom the flagpole compare?

2. OBTUSE TRIANGLES Don notices thatthe side opposite the right angle in aright triangle is always the longest ofthe three sides. Is this also true of theside opposite the obtuse angle in anobtuse triangle? Explain.

3. STRING Jake built a triangularstructure with three black sticks. Hetied one end of a string to vertex Mand the other end to a point on the stick opposite M, pulling the string taut. Prove that the length of the string cannot exceed the longer of thetwo sides of the structure.

4. SQUARES Matthew has three differentsquares. He arranges the squares toform a triangle as shown. Based on the information, list the squares in order from the one with the smallestperimeter to the one with the largestperimeter.

CITIES For Exercises 5 and 6, use the following information.Stella is going to Texas to visit a friend.As she was looking at amap to see where shemight want to go, she noticed the cities Austin, Dallas, and Abileneformed a triangle. She wanted to determinehow the distances between the cities wererelated, so she used a protractor to measuretwo angles.

5. Based on the information in the figure,which of the two cities are nearest toeach other?

6. Based on the information in the figure,which of the two cities are farthest apartfrom each other?

59˚

64˚

Abilene

Dallas

Austin

54˚47˚

3

1 2

string

M

05-42 Geo-05-873962 4/3/06 4:57 PM Page 17

Page 31: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 5 26 Glencoe Geometry

Word Problem PracticeIndirect Proof

NAME ______________________________________________ DATE ____________ PERIOD _____

5-3C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. CANOES Thirty-five students went on a canoeing expedition. They rented 17 canoes for the trip. Use an indirectproof to show that at least one canoehad more than two students in it.

2. AREA The area of the United States isabout 6,000,000 square miles. The areaof Hawaii is about 11,000 square miles.Use an indirect proof to show that atleast one of the fifty states has an areagreater than 120,000 square miles.

3. CONSECUTIVE NUMBERS David was trying to find a common factor other than 1 between various pairs of consecutive integers. Write an indirect proof to show David that two consecutive integers do not share a common factor other than 1.

4. WORDS The words accomplishment,counterexample, and extemporaneous allhave 14 letters. Use an indirect proof toshow that any word with 14 letters mustuse a repeated letter or have two lettersthat are consecutive in the alphabet.

LATTICE TRIANGLES For Exercises 5and 6, use the following information.A lattice point is a point whose coordinatesare both integers. A lattice triangle is atriangle whose vertices are lattice points. Itis a fact that a lattice triangle has an areaof at least 0.5 square units.

5. Suppose �ABC has a lattice point in itsinterior. Show that the lattice trianglecan be partitioned into three smallerlattice triangles.

6. Prove indirectly that a lattice trianglewith area 0.5 square units contains nolattice point. (Being on the boundarydoes not count as inside.)

y

xO

A

B

C

5

5

05-42 Geo-05-873962 4/3/06 4:57 PM Page 26

Page 32: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 5 33 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeThe Triangle Inequality

NAME ______________________________________________ DATE ____________ PERIOD _____

5-4

Less

on

5-4

1. STICKS Jamila has 5 sticks of lengths2, 4, 6, 8, and 10 inches. Using threesticks at a time as the sides of triangles,how many triangles can she make?

Use the figure at the right for Exercises 2 and 3.

2. PATHS To get to the nearest supermarket,Tanya must walkover a railroad track. There are two places where she can cross thetrack (points Aand B). Which path is longer? Explain.

3. PATHS While out walking one dayTanya finds a third place to cross therailroad tracks. Show that the paththrough point C is longer than the path through point B.

4. CITIES The distance between New YorkCity and Boston is 187 miles and thedistance between New York City andHartford is 97 miles. Hartford, Boston,and New York City form a triangle on amap. What must the distance betweenBoston and Hartford be greater than?

TRIANGLES For Exercises 5–7, use thefollowing information.The figure shows an equilateral triangleABC and a point P outside the triangle.

5. Draw the figure that is the result of turning the original figure 60°counterclockwise about A. Denote by P�, the image of P under this turn.

6. Note that P���B� is congruent to P�C�. It isalso true that P�P��� is congruent to P�A�.Why?

7. Show that P�A�, P�B�, and P�C� satisfy thetriangle inequalities.

B ,

C

P

B

A

Tanya’s home

Supermarket

Railroad

A B C

05-42 Geo-05-873962 4/3/06 4:57 PM Page 33

Page 33: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 5 40 Glencoe Geometry

Word Problem PracticeInequalities Involving Two Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

5-5C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. CLOCKS The minute hand of agrandfather clock is 3 feet long and the hour hand is 2 feet long. Is thedistance between their ends greater at 3:00 or at 8:00?

2. FERRIS WHEEL A Ferris wheel hascarriages located at the 10 vertices of a regular decagon.

Which carriages are farther away from carriage number 1 than carriagenumber 4?

3. WALKWAY Tyree wants to make twoslightly different triangles for hiswalkway. He has three pieces of wood to construct the frame of his triangles.After Tyree makes the first concretetriangle, he adjusts two sides of thetriangle so that the angle they create is smaller than the angle in the firsttriangle. Explain how this changes thetriangle.

4. MOUNTAIN PEAKS Emily lives thesame distance from three mountainpeaks: High Point, Topper, and CloudNine. For a photography class, Emilymust take a photograph from her housethat shows two of the mountain peaks.Which two peaks would she have thebest chance of capturing in one image?

RUNNERS For Exercises 5 and 6, usethe following information.A photographer is taking pictures of threetrack stars, Amy, Noel, and Beth. Thephotographer stands on a track, which isshaped like a rectangle with semicircles on both ends.

5. Based on the information in the figure,list the runners in order from nearest to farthest from the photographer.

6. Explain how to locate the point alongthe semicircular curve that the runnersare on that is farthest away from thephotographer.

118˚

36˚146˚

Photographer

Amy

Noel

Beth

Emily

CloudNine

HighPoint

Topper

12 miles

9 m

iles

10 miles1

2

3

4

56

7

8

9

10

05-42 Geo-05-873962 4/3/06 4:58 PM Page 40

Page 34: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 10 Glencoe Geometry

Word Problem PracticeAngles of Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

6-1C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room builtby Buontalenti called the Tribune (LaTribuna in Italian). This room is shapedlike a regular octagon.

What angle do consecutive walls of theTribune make with each other?

2. BOXES Jasmine is designing boxes shewill use to ship her jewelry. She wants to shape the box like a regular polygon.In order for the boxes to pack tightly,she decides to use a regular polygon thathas the property that the measure of itsinterior angles is half the measure of itsexterior angles. What regular polygonshould she use?

3. THEATER A theater floor plan is shownin the figure. The upper five sides arepart of a regular dodecagon.

Find m�1.

4. ARCHEOLOGY Archeologistsunearthed parts of two adjacent walls of an ancient castle.

Before it was unearthed, they knew fromancient texts that the castle was shapedlike a regular polygon, but nobody knewhow many sides it had. Some said 6,others 8, and some even said 100. Fromthe information in the figure, how manysides did the castle really have?

POLYGON PATH For Exercises 5–7, usethe following information.In Ms. Rickets’ math class, students made a “polygon path” that consists of regularpolygons of 3, 4, 5, and 6 sides joinedtogether as shown.

5. Find m�2 and m�5.

6. Find m�3 and m�4.

7. What is m�1?

2

1

34

5

24˚

stage1

La Tribuna

05-56 Geo-06-873963 4/3/06 2:05 PM Page 10

Page 35: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 17 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeParallelograms

NAME ______________________________________________ DATE ____________ PERIOD _____

6-2

Less

on

6-2

1. WALKWAY A walkway is made byadjoining four parallelograms as shown.

Are the end segments a and e parallel toeach other? Explain.

2. DISTANCE Gracie, Kenny, Teresa, andTravis live at the four corners of blockshaped like a parallelogram. Gracie lives 3 miles away from Kenny. How farapart do Teresa and Travis live fromeach other?

3. SOCCER Four soccer players are locatedat the corners of a parallelogram. Twoof the players in opposite corners are the goalies. In order for goalie A to beable to see the three others, she must be able to see a certain angle x in herfield of vision.

What angle does the other goalie have tobe able to see in order to keep an eye onthe other three players?

4. VENN DIAGRAMS Make a Venndiagram showing the relationshipbetween squares, rectangles, andparallelograms.

SKYSCRAPERS For Exercises 5 and 6,use the following information.On vacation, Tony’s family took ahelicopter tour of thecity. The pilot said the newest building in the city was thebuilding with this topview. He told Tonythat the exteriorangle by the front entrance is 72º. Tonywanted to know more about the building,so he drew this diagram and used hisgeometry skills to learn a few more things.The front entrance is next to vertex B.

5. What are the measures of the fourangles of the parallelogram?

6. How many pairs of congruent trianglesare there in the figure? What are they?

A B

C D

E

72˚

Goalie B Player A

Goalie APlayer B

TeresaTravis

Gracie Kenny

a

e

05-56 Geo-06-873963 4/3/06 2:06 PM Page 17

Page 36: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 24 Glencoe Geometry

Word Problem PracticeTests for Parallelograms

NAME ______________________________________________ DATE ____________ PERIOD _____

6-3C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. BALANCING Nikia, Madison, Angela,and Shelby are balancing themselves on an “X”-shaped floating object. Tobalance themselves, they want to make themselves the vertices of aparallelogram.

In order to achieve this, do all four ofthem have to be the same distance fromthe center of the object? Explain.

2. COMPASSES Two compass needlesplaced side by side on a table are both 2 inches long and point due north. Dothey form the sides of a parallelogram?

3. FORMATION Four jets are flying information. Three of the jets are shown in the graph. If the four jets are locatedat the vertices of a parallelogram, whatare the three possible locations of themissing jet?

4. STREET LAMPS When a coordinateplane is placed over the Harrisville townmap, the four street lamps in the centerare located as shown. Do the four lampsform the vertices of a parallelogram?Explain.

PICTURE FRAME For Exercises 5–7, usethe following information.Aaron is making a wooden picture frame inthe shape of a parallelogram. He has twopieces of wood that are 3 feet long and twothat are 4 feet long.

5. If he connects the pieces of wood at their ends to each other, in what ordermust he connect them to make aparallelogram?

6. How many different parallelogramscould he make with these four lengths of wood?

7. Explain something Aaron might do to specify precisely the shape of theparallelogram.

5

5 y

xO–5

–5

5

5

y

xO

Shelby

Madison

NikiaAngela

05-56 Geo-06-873963 4/3/06 2:06 PM Page 24

Page 37: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 31 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeRectangles

NAME ______________________________________________ DATE ____________ PERIOD _____

6-4

Less

on

6-4

1. FRAMES Jalen makes the rectangularframe shown

In order to make sure that it is arectangle, Jalen measures the distancesBD and AC. How should these twodistances compare if the frame is arectangle?

2. BOOKSHELFS A bookshelf consists of two vertical planks with five horizontalshelves. Are each of thefour sections for booksrectangles? Explain.

3. LANDSCAPER A landscaper is markingoff the corners of a rectangular plot ofland. Three of the corners are in place as shown.

What are the coordinates of the fourthcorner?

4. SWIMMING POOLS Antonio isdesigning a swimming pool on acoordinate grid. Is it a rectangle?Explain.

PATTERNS For Exercises 5 and 6, usethe following information.Veronica made the pattern shown out of 7rectangles with four equal sides. The sidelength of each rectangle is written insidethe rectangle.

5. How many rectangles can be formedusing the lines in this figure?

6. If Veronica wanted to extend her patternby adding another rectangle with 4equal sides to make a larger rectangle,what are the possible side lengths ofrectangles that she can add?

1 1

2 3

5

8

5

y

xO

5

5y

xO–5

–5

A B

D C

05-56 Geo-06-873963 4/3/06 2:06 PM Page 31

Page 38: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 40 Glencoe Geometry

Word Problem PracticeRhombi and Squares

NAME ______________________________________________ DATE ____________ PERIOD _____

6-5C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. TRAY RACKS A tray rack looks like aparallelogram from the side. The levelsfor the trays are evenly spaced.

What two labeled points form a rhombuswith base AA�?

2. SLICING Charles cuts a rhombus alongboth diagonals. He ends up with fourcongruent triangles. Classify thesetriangles as acute, obtuse, or right.

3. WINDOWS The edges of a window aredrawn in the coordinate plane.

Determine whether the window is asquare or a rhombus.

4. SQUARES Mackenzie cut a squarealong its diagonals to get four congruentright triangles. She then joined two ofthem along their long sides. Show thatthe resulting shape is a square.

DESIGN For Exercises 5 and 6, use thefollowing information.Tatianna made the design shown. She used32 congruent rhombi to create the flower-like design at each corner.

5. What are the angles of the cornerrhombi?

6. What kinds of quadrilaterals are thedotted and checkered figures?

y

xO

AB

CDE

FG

H

B ,C ,D ,E ,F ,G ,H ,

A20 inches

AB = 4 inches,

05-56 Geo-06-873963 4/3/06 2:06 PM Page 40

Page 39: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 47 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeTrapezoids

NAME ______________________________________________ DATE ____________ PERIOD _____

6-6

Less

on

6-6

1. PERSPECTIVE Artists use differenttechniques to make things appear to be3-dimensional when drawing in twodimensions. Kevin drew the walls of aroom. In real life, all of the walls arerectangles. In what shape did he drawthe side walls to make them appear 3-dimensional?

2. PLAZA In order to give the feeling of spaciousness, an architect decides to make a plaza in the shape of anisosceles trapezoid. Three of the fourcorners of the plaza are shown in thecoordinate plane. If the fourth corner is in the first quadrant, what are itscoordinates?

3. AIRPORTS A simplified drawing of the reef runway complex at HonoluluInternational Airport is shown below.

How many trapezoids are there in thisimage?

4. LIGHTING A light outside a roomshines through the door and illuminatesa trapezoidal region ABCD on the floor.

Under what circumstances wouldtrapezoid ABCD be isosceles?

RISERS For Exercises 5 and 6, use thefollowing information.A riser is designed to elevate a speaker. Theriser consists of 4 trapezoidal sections thatcan be stacked one on top of the other toproduce trapezoids of varying heights.

All of the stages have the same height. If allfour stages are used, the width of the top ofthe riser is 10 feet.

5. If only the bottom two stages are used,what is the width of the top of theresulting riser?

6. What would be the width of the riser ifthe bottom three stages are used?

20 feet

10 feet

A B

D C

y

xO

05-56 Geo-06-873963 4/3/06 2:06 PM Page 47

Page 40: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 6 54 Glencoe Geometry

Word Problem PracticeCoordinate Proof and Quadrilaterals

NAME ______________________________________________ DATE ____________ PERIOD _____

6-7C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. DRAFTING An engineer is making adrawing of an isosceles trapezoid in acoordinate plane. She places three of the vertices at (0, 0), (a, 0), and (b, c),where 0 b 0.5a and c � 0. Where in the first quadrant can she place thefourth point?

2. ZIGZAGS If the zigzag pattern ofparallelograms is continued by addingone more parallelogram to the right,what would be the coordinates of thenew parallelogram’s vertices?

3. SUPPORTS The four plotted pointsrepresent the locations of four supportcolumns for a building.

Classify the quadrilateral whose verticesare at these four points. Explain.

4. SQUARES Prove that the quadrilateralwith vertices (a, b), (�b, a), (�a, �b),and (b, �a) is a square, where a and bare positive numbers.

AXES For Exercises 5–7, use thefollowing information.Sara used a geometry program to drawquadrilateral ABCD on a coordinate graphthat did not have any other lines except thex-axis and y-axis. She was able to drag thevertices to create different quadrilaterals.Let a, b, c, and d be positive integers andconsider the points A = (a, 0), B = (0, b),C = (�c, 0), and D = (0, �d).

5. Describe the conditions of a, b, c, and dso that quadrilateral ABCD is a square.

6. Describe the conditions of a, b, c, and dso that quadrilateral ABCD is arhombus.

7. Describe the conditions of a, b, c, and dso that quadrilateral ABCD is anisosceles trapezoid.

x

y

O

y

xO

05-56 Geo-06-873963 4/3/06 2:06 PM Page 54

Page 41: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

1. MODELS Luke wants to make a scalemodel of a Boeing 747 jetliner. He wantsevery foot of his model to represent 50feet. Complete the following table.

(Source: www.boeing.com)

2. RATIONS Sixteen students went on a week-long hiking trip. They broughtwith them 320 specially baked, protein-rich, cookies. What is the ratio of cookiesto students?

3. PHOTOGRAPHS Tracy is 4 feet tall and her father is 6 feet tall. In a photograph of the two of themstanding side by side, Tracy’s image is 2 inches tall.

Although their images are much smaller,the ratio of their heights remains thesame. How tall is Tracy’s father’s imagein the photo?

4. CARS A car company builds twoversions of one of its models—a sedanand a station wagon. The ratio of sedansto station wagons is 11 : 2. A freighterbegins unloading the cars at a dock.Tom counts 18 station wagons and thenoverhears a dock worker call out, “Okay,that’s all of the wagons . . . bring out the sedans!” How many sedans were onthe ship?

MAPS For Exercises 5–7, use thefollowing information.Carlos makes a map of his neighborhood for a presentation. The scale of his map is 1 inch : 125 feet.

5. How many feet do 4 inches represent onthe map?

6. Carlos lives 250 feet away from Andrew.How many inches separate Carlos’ homefrom Andrew’s on the map?

7. During a practice run in front of hisparents, Carlos realizes that his map is far too small. He decides to make his map 5 times as large. What would be the scale of the larger map?

6 ft4 ft

Chapter 7 10 Glencoe Geometry

Word Problem PracticeProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

Actual ModelPart length (in.) length (in.)

Wing Span 2,537

Length 2,782

Tail Height 392 7.84

05-42 Geo-07-873964 4/12/06 8:44 PM Page 10

Page 42: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 7 18 Glencoe Geometry

Word Problem PracticeSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. PANELS When closed, an entertainmentcenter is made of four square panels.The three smaller panels are congruentsquares.

What is the scale factor of the largersquare to one of the smaller squares?

2. DOWNSPOUTS During a storm, one of the downspouts on Mr. Herrera’shouse was broken and needed to bereplaced. Unfortunately, the downspoutwas too damaged to measure its lengthand it was too difficult to measure theheight of the gutter. Luckily, Mr. Herrerahad a scale model of his house. If the downspout in the model was 1�

12� feet

long and the scale factor was 20, howlong was the actual downspout?

3. ORIGAMI Baxter uses an 8-inch square piece of origami paper to makean origami model of a chicken. Whenfinished, the chicken stands 4 incheshigh. Baxter wants to make anotherorigami chicken, only this time he wants to make it 12 inches high instead.What size piece of paper should he useto do this?

4. ENLARGING Camille wants to make a pattern for a four-pointed star withdimensions twice as long as the oneshown. Help her by drawing a star withdimensions twice as long on the gridbelow.

BIOLOGY For Exercises 5–7, use thefollowing information.A paramecium is a small single-cellorganism. The paramecium magnified belowis actually one tenth of a millimeter long.

5. If you want to make a photograph of theoriginal paramecium so that its image is1 centimeter long, by what scale factorshould you magnify it?

6. If you want to make a photograph of theoriginal paramecium so that its image is15 centimeters long, by what scale factorshould you magnify it?

7. By approximately what scale factor hasthe paramecium been enlarged to makethe image shown?

05-42 Geo-07-873964 4/12/06 8:44 PM Page 18

Page 43: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 7 25 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3

Less

on

7-3

1. MINIATURES Marla likes her chair so much that she decides to make aminiature replica of it for her pethamster. Find the value of x.

2. MODELS Jim has a scale model of hissailboat. The figure shows drawings ofthe original sailboat and the model.Find x.

3. GEOMETRY Georgia draws a regularpentagon and starts connecting itsvertices to make a 5-pointed star. Afterdrawing three of thelines in the star, shebecomes curiousabout two trianglesthat appear in thefigure, �ABC and�BCE. They look similar to her. Provethat this is the case.

4. SHADOWS A radio tower casts ashadow 8 feet long at the same time that a vertical yardstick casts a shadowhalf an inch long. How tall is the radiotower?

MOUNTAIN PEAKS For Exercises 5 and6, use the following information.Gavin and Brianna want to know how far amountain peak is from their houses. Theymeasure the angles between the line of siteto the peak and to each other’s houses andcarefully make the drawing shown.

The actual distance between Gavin and Brianna’s house is 1�

12� miles.

5. What is the actual distance of themountain peak from Gavin’s house?Round your answer to the nearest tenth of a mile.

6. What is the actual distance of themountain peak from Brianna’s house?Round your answer to the nearest tenth of a mile.

Gavin

Brianna

Peak

2 in.

2.015 in.0.246 in.

90˚83˚

A

B

D

E

C

52˚

203 in.

10.15 in. 8 in.52˚

x in.

14”

3.5”

15”

x

05-42 Geo-07-873964 4/12/06 8:44 PM Page 25

Page 44: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 7 32 Glencoe Geometry

Word Problem PracticeParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

1. CARPENTRY Jake isfixing an A-frame.He wants to add ahorizontal supportbeam halfway up and parallel to the ground. Howlong should thisbeam be?

2. STREETS In the diagram, Cay Streetand Bay Street are parallel. Find x.

3. JUNGLE GYMS Prassad is building atwo-story jungle gym according to theplans shown. Find x.

4. FIREMEN A cat is stuck in a treeand firemen try torescue it. Basedon the figure, if afireman climbs to the top of theladder, how faraway is the cat?

EQUAL PARTS For Exercises 5 and 6,use the following information.Nick has a stick that he would like to divide into 9 equal parts. He places it on a piece of grid paper as shown. The grid paper is ruled so that vertical andhorizontal lines are equally spaced.

5. Explain how he can use the grid paperto help him find where he needs to cutthe stick.

6. Suppose Nick wants to divide his stickinto 5 equal parts utilizing the gridpaper. What can he do?

Meeeeowww!

30 ft.

40 ft.46 ft.

x

8 ft. 8 ft.

10 ft.

24 ft

.

10 ft.x

Cay St.

1 km 1.4 km

0.8 km

Bay St.

Dale

St. Earl St.

(not drawn to scale)

x

8 feet

05-42 Geo-07-873964 4/12/06 8:45 PM Page 32

Page 45: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 7 39 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5

Less

on

7-5

1. JOGGING Macy wants to jog aroundTriangle Park. On a scale map, the parkhas a perimeter of 11 inches. The scaleof the map is 1 inch : 100 yards. What isthe perimeter of the actual park?

2. TENTS Jana went camping and stayedin a tent shaped like a triangle. In aphoto of the tent, the base of the tent is6 inches and the altitude is 5 inches. Theactual base was 12 feet long. What wasthe height of the actual tent?

3. PLAYGROUND The playground atHank’s school has a large right trianglepainted in the ground. Hank starts at the right angle corner and walkstoward the opposite side along an anglebisector and stops when he gets to thehypotenuse.

How much farther from Hank is point Bversus point A?

4. FLAG POLES A flag pole attached tothe side of a building is supported with a network of strings as shown in thefigure.

The rigging is done so that AE � EF,AC � CD, and AB � BC. What is theratio of CF to BE?

COPIES For Exercises 5 and 6, use thefollowing information.Gordon made a photocopy of a page from his geometry book to enlarge one of thefigures. The actual figure that he copied isshown below.

The photocopy came out poorly. Gordoncould not read the numbers on thephotocopy, although the triangle itself was clear. Gordon measured the base of the enlarged triangle and found it to be 200 millimeters.

5. What is the length of the drawn altitudeof the enlarged triangle? Round youranswer to the nearest millimeter.

6. What is the length of the drawn medianof the enlarged triangle? Round youranswer to the nearest millimeter.

39 mm

Med

ian

Altit

ude

30 mm

29 mm

A BC

DF

E

A

B

45˚

30 ft

40 ft

50 ft

x

05-42 Geo-07-873964 4/12/06 8:45 PM Page 39

Page 46: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

8-1

Chapter 8 10 Glencoe Geometry

1. SQUARES Wilma has a rectangle ofdimensions by w. She would like toreplace it with a square that has thesame area. What is the side length of thesquare with the same area as Wilma’srectangle?

2. EQUALITY Gretchen computed thegeometric mean of two numbers. One ofthe numbers was 7 and the geometricmean turned out to be 7 as well. Whatwas the other number?

3. VIEWING ANGLE A photographerwants to take a picture of a beach front.His camera has a viewing angle of 90°and he wants to make sure two palmtrees located at points A and B in thefigure are just inside the edges of thephotograph.

He walks out on a walkway that goesover the ocean to get the shot. If hiscamera has a viewing angle of 90º, atwhat distance down the walkway shouldhe stop to take his photograph?

4. EXHIBITIONS A museum has a famousstatue on display. The curator places thestatue in the corner of a rectangularroom and builds 15-foot-long railing infront of the statue. Use the informationbelow to find how close visitors will beable to get to the statue.

CLIFFS For Exercises 5–7, use thefollowing information.A bridge connects to a tunnel as shown inthe figure. The bridge is 180 feet above theground. At a distance of 235 feet along thebridge out of the tunnel, the angle to thebase and summit of the cliff is a right angle.

5. What is the height of the cliff? Round tothe nearest whole number.

6. How high is the cliff from base tosummit? Round to the nearest wholenumber.

7. What is d? Round to the nearest wholenumber.

Cliff

235 ft

180

ft

d x

h

Statue12 ft

15 ft9 ft

x

Wal

kway

90 ft 40 ftA B

x

Wal

kway

A B

x

Word Problem PracticeGeometric Mean

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1-55 Geo-08-873965 3/2/06 10:01 AM Page 10

Page 47: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 8 17 Glencoe Geometry

Less

on

8-2

8-2 Word Problem PracticeThe Pythagorean Theorem and Its Converse

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. SIDEWALKS Construction workers arebuilding a marble sidewalk around apark that is shaped like a right triangle.Each marble slab adds 2 feet to thelength of the sidewalk. The workers findthat exactly 1071 and 1840 slabs arerequired to make the sidewalks along theshort sides of the park. How many slabsare required to make the sidewalk thatruns along the long side of the park?

2. RIGHT ANGLES Clyde makes atriangle using three sticks of lengths 20inches, 21 inches, and 28 inches. Is thetriangle a right triangle? Explain.

3. TETHERS To help support a flag pole, a50-foot-long tether is tied to the pole ata point 40 feet above the ground. Thetether is pulled taut and tied to ananchor in the ground. How far awayfrom the base of the pole is the anchor?

4. FLIGHT An airplane lands at an airport60 miles east and 25 miles north ofwhere it took off.

How far apart are the two airports?

PYTHAGOREAN TRIPLES For Exercises5–7, use the following information.Ms. Jones assigned her fifth-periodgeometry class the following problem.Let m and n be two positive integers with m > n. Let a = m2 – n2, b = 2mn, and c = m2 + n2.

5. Show that there is a right triangle withside lengths a, b, and c.

6. Complete the following table.

m n a b c2 1 3 4 53 13 24 14 24 35 1

7. Find a Pythagorean triple thatcorresponds to a right triangle with ahypotenuse 252 = 625 units long. (Hint:Use the table you completed for Exercise6 to find two positive integers m and nwith m > n and m2 � n2 � 625.)

60 mi

25 mi

1-55 Geo-08-873965 3/2/06 10:05 AM Page 17

Page 48: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 8 25 Glencoe Geometry

Less

on

8-3

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

8-3 Word Problem PracticeSpecial Right Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

1. ORIGAMI A square piece of paper 150millimeters on a side is folded in halfalong a diagonal. The result is a 45°-45°-90° triangle. What is the length of thehypotenuse of this triangle?

2. ESCALATORS A 40-foot-long escalatorrises from the first floor to the secondfloor of a shopping mall. The escalatormakes a 30° angle with the horizontal.

How high above the first floor is thesecond floor?

3. HEXAGONS A box of chocolates shapedlike a regular hexagon is placed snuglyinside of a rectangular box as shown inthe figure.

If the side length of the hexagon is 3inches, what are the dimensions of therectangular box?

4. WINDOWS A large stained glasswindow is constructed from six 30°-60°-90° triangles as shown in the figure.

What is the height of the window?

MOVIES For Exercises 5–7, use thefollowing information.Kim and Yolanda are watching a movie in amovie theater. Yolanda is sitting x feet fromthe screen and Kim is 15 feet behind Yolanda.

The angle that Kim’s line of sight to the topof the screen makes with the horizontal is30°. The angle that Yolanda’s line of sight tothe top of the screen makes with thehorizontal is 45°.

5. How high is the top of the screen interms of x?

6. What is ?

7. How far is Yolanda from the screen?Round your answer to the nearest tenth.

x�15�x

30˚ 45˚15 ft x ft

3 m

40 ft

30˚

? ft

1-57 Geo-08-873965 5/25/06 2:28 PM Page 25

Page 49: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 8 32 Glencoe Geometry

8-4NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

Word Problem PracticeTrigonometry

1. RADIO TOWERS Kay is standing neara 200-foot-high radio tower.

Use the information in the figure todetermine how far Kay is from the top ofthe tower. Express your answer as atrigonometric function.

2. RAMPS A 60-foot ramp rises from thefirst floor to the second floor of a parkinggarage. The ramp makes a 15° anglewith the ground.

How high above the first floor is thesecond floor? Express your answer as atrigonometric function.

3. TRIGONOMETRY Melinda and Walterwere both solving the same trigonometryproblem. However, after they finishedtheir computations, Melinda said theanswer was 52 sin 27° and Walter saidthe answer was 52 cos 63°. Could theyboth be correct? Explain.

4. LINES Jasmine draws line m on acoordinate plane.

What angle does m make with the x-axis? Round your answer to thenearest degree.

NEIGHBORS For Exercises 5–7, use thefollowing information.Amy, Barry, and Chris live on the sameblock. Chris lives up the street and aroundthe corner from Amy, and Barry lives at thecorner between Amy and Chris. The threehomes make a right triangle.

5. Give two trigonometric expressions forthe ratio of Barry’s distance from Amy toChris’ distance from Amy.

6. Give two trigonometric expressions forthe ratio of Barry’s distance from Christo Amy’s distance from Chris.

7. Give a trigonometric expression for theratio of Amy’s distance from Barry toChris’ distance from Barry.

64˚

Barry

Chris

Amy26˚

m

x

y

O-5

5

5

? ft

60 ft

15˚

200 ft ? ft

49˚

1-57 Geo-08-873965 4/14/06 9:16 AM Page 32

Page 50: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

7-57-5

Chapter 8 39 Glencoe Geometry

Less

on

8-5

8-5 Word Problem PracticeAngles of Elevation and Depression

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. LIGHTHOUSES Sailors on a ship at seaspot the light from a lighthouse. Theangle of elevation to the light is 25°.

The light of the lighthouse is 30 metersabove sea level. How far from the shoreis the ship? Round your answer to thenearest meter.

2. RESCUE A hiker dropped his backpackover one side of a canyon onto a ledgebelow. Because of the shape of the cliff, hecould not see exactly where it landed.

From the other side, the park rangerreports that the angle of depression tothe backpack is 32°. If the width of thecanyon is 115 feet, how far down did thebackpack fall? Round your answer to thenearest whole number.

3. AIRPLANES The angle of elevation toan airplane viewed from the controltower at an airport is 7°. The tower is200 feet high and the pilot reports thatthe altitude is 5200 feet. How far awayfrom the control tower is the airplane?Round your answer to the nearest foot.

4. PEAK TRAM The Peak Tram in HongKong connects two terminals, one at thebase of a mountain, and the other at thesummit. The angle of elevation of theupper terminal from the lower terminalis about 15.5°. The distance between thetwo terminals is about 1365 meters.About how much higher above sea levelis the upper terminal compared to thelower terminal? Round your answer tothe nearest meter.

HELICOPTERS For Exercises 5–7, usethe following information.Jermaine and John are watching ahelicopter hover above the ground.

Jermaine and John are standing 10meters apart.

5. Find two different expressions that canbe used to find the h, height of thehelicopter.

6. Equate the two expressions you foundfor Exercise 5 to solve for x. Round youranswer to the nearest hundredth.

7. How high above the ground is thehelicopter? Round your answer to thenearest hundredth.

48˚ 55˚

(Not drawn to scale)

Helicopter

Jasper John10m

h

x

32˚

115 ft

? ft

Backpack

25˚30m

?

1-55 Geo-08-873965 3/2/06 10:17 AM Page 39

Page 51: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 8 46 Glencoe Geometry

7-67-68-6 Word Problem PracticeThe Law of Sines

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. ALTITUDES In triangle ABC, thealtitude to side AB is drawn.

Give two expressions for the length ofthe altitude in terms of a, b, and the sineof the angles A and B.

2. MAPS Three cities form the vertices ofa triangle. The angles of the triangle are40°, 60°, and 80°. The two most distantcities are 40 miles apart. How close arethe two closest cities? Round youranswer to the nearest tenth of a mile.

3. PHOTOS Greg took a photograph of theview from his city apartment. Thebuilding on the left is the Rocket Towerand the building on the right is theCloud Scratcher.

Greg’s camera has a 60° viewing angle.Greg knows that he is 2 miles from theCloud Scratcher and that the RocketTower is 3 miles from the CloudScatcher. How far is Greg from theRocket Tower? Round your answer to thenearest hundredth.

4. BOATING A boat heads out to sea froma port that sits along a straightshoreline. The boat heads in a directionthat makes a 70° angle with theshoreline. After sailing for 3 miles, theskipper looks back at the shore and seeshis house. The house, like the port, alsosits on the shore. The lines of sight tothe port and to his home make an 80°angle. How far is the skipper’s homefrom the port? Round your answer to thenearest tenth of a mile.

ISLANDS For Exercises 5 and 6, use thefollowing information.Oahu is a Hawaiian Island. Off of thecoast of Oahu, thereis a very tiny islandknown asChinaman’s Hat.Keoki and Malia areobservingChinaman’s Hatfrom locations 5kilometers apart.Use the information in the figure to answerthe following questions.

5. How far is Keoki from Chinaman’s Hat?Round your answer to the nearest tenthof a kilometer.

6. How far is Malia from Chinaman’s Hat?Round your answer to the nearest tenthof a kilometer.

Ka’a’awa

Keoki Chinaman’sHat

5 km

Malia

Kahalu’u

22.3˚

49.5˚

house

port

70˚

80˚

A

ab

B

C

1-57 Geo-08-873965 4/14/06 9:23 AM Page 46

Page 52: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 8 54 Glencoe Geometry

0-70-7C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

8-7 Word Problem PracticeThe Law of Cosines

NAME ______________________________________________ DATE ____________ PERIOD _____

1. RIGHT TRIANGLES Triangle ABC is aright triangle with right angle at B. Leta be the length of the side opposite A, bbe the length of the side opposite B, andc be the length of the side opposite C.

Rewrite the Law of Cosines with respectto the right angle B in simplest form.

2. LANDSCAPING Hanna wants to fencea triangular lot as shown. What is thelength of the missing side? Round youranswer to the nearest foot.

3. STATUES Gail was visiting an artgallery. In one room, she stood so thatshe had a view of two statues, one of aman, and the other of a woman. She was40 feet from the statue of the woman,and 35 feet from the statue of the man.The angle created by the lines of sight tothe two statues was 21°. What is thedistance betweenthe two statues?Round youranswer to thenearest tenth.

4. CARS Two cars start moving from thesame location. They head straight, but indifferent directions. The angle betweenwhere they are heading is 43°. The firstcar travels 20 miles and the second cartravels 37 miles. How far apart are thetwo cars? Round your answer to thenearest tenth.

CITIES For Exercises 5–7, use thefollowing information.The cities of Denver, Oklahoma City, andAlbuquerque form the vertices of a triangle.

Use the information in the figure and roundyour answers to the nearest tenth of adegree.

5. What is the measure of the angle atAlbuquerque?

6. What is the measure of the angle atOklahoma City?

7. What is the measure of the angle atDenver?

Denver

OklahomaCity

Albuquerque

(Not drawn to scale)

336

mi

515 mi

509 mi

Statue ofa man

Statue of a woman

35 ft

40 ft

21˚

80˚ 85 ft 76 ft

A

a

bc

B C

1-55 Geo-08-873965 3/2/06 12:00 PM Page 54

Page 53: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 10 Glencoe Geometry

9-1 Word Problem PracticeReflections

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. REFLECTIONS Vincent is making a starwith a horizontal line of symmetry.Complete the star by drawing thereflected image of the figure over line m.

2. LINES OF SYMMETRY Maria placed apaper cutout on a table and then left toget some glue. Her friend James flippedover the cutout without telling Maria.Still, when Maria came back it wasimpossible for her to be able to see thatanything had been changed. Draw a linethrough the figure that represents theline over which James must have flippedthe figure.

3. SYMMETRY Martha made the figureshown. How many lines of symmetrydoes the figure have?

4. INTERIOR DESIGN Wilfred hired aninterior designer to layout the furniturein his bedroom. The designer producedthe plan shown in the figure.Unfortunately,Wilfred’swindow islocated on theopposite wallfrom the plan.Wilfreddecides to justreflect theplan over thevertical line through the center of theroom. Draw the reflected plan.

TRIANGLES For Exercises 5 and 6, usethe following information.Casey drew this triangle on the coordinateplane.

5. What are the vertices of the image ofthis triangle if it is reflected over the y-axis?

6. What are the vertices of the image ofthis triangle if it is reflected over theline y = x?

x

y

O 5

5

Bed

Lamp

Desk

Win

dow

TableBureau

m

1-48 Geo-09-873966 4/14/06 10:03 AM Page 10

Page 54: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 17 Glencoe Geometry

Less

on

9-2

9-2 Word Problem PracticeTranslations

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. TRANSLATIONS Wynette wants to seethe translation of the five-sided figureshown. Draw the translation so that theindicated vertex is translated to thelocation of the dot.

2. WALLPAPER A wallpaper designconsists of repeated translations of asingle isosceles triangle. The pattern isshown overlaid on a coordinate plane.The space above the triangle around thecoordinate (5, 1) should be filled with amissing triangle. What are thecoordinates of the vertices of the trianglethat fill this space consistently with therest of the pattern?

3. REFLECTIONS Gus reflects an objecttwice. The first step is to reflect it overthe line y = –1. Then Gus completes thecomposite reflection by reflecting it overthe line y = 1. The net effect is atranslation of the object. Describe thistranslation.

4. A TALE OF TWO TRANSLATIONSLacy performs the translation (x, y) → (x + 5, y + 3) to an object in thecoordinate plane. Kyle performs thetranslation (x, y) → (x – 4, y + 2) to thesame object after Lacy. What singletranslation could have been done toachieve the same effect as Lacy andKyle’s combined translations? Would theresult have been different if Kyle did histranslation first?

SQUARES AND CIRCLES For Exercises5 and 6, use the following figure.

5. The image of square S under atranslation is square S�. Describe thistranslation.

6. Draw the image of the circle C under thesame translation that you described inExercise 5.

y

xO

5

5-5

-5S

C

S‘xO 5

5

y

1-48 Geo-09-873966 4/14/06 10:09 AM Page 17

Page 55: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 26 Glencoe Geometry

1. ROTATIONS What is the order ofrotational symmetry of the figure shownbelow?

2. FLYERS Nicki is making a flyer thatcontains a large capital “M”.

She decides that she needs to rotate the“M” clockwise by 60°. Draw the rotatedimage.

3. REFLECTIONS Marge reflects an objecttwice. The first step is to reflect it in theline y = 0. Then Marge completes thecomposite reflection by reflecting it inthe line y = x. The net effect is a rotationof the object. Describe this rotation.

4. MAGNITUDES A circular dial with thedigits 0 through 9 evenly spaced aroundits edge can be rotated clockwise 36°.How many times would you have toperform this rotation in order to bringthe dial back to its original orientation?

PLACE SETTINGS For Exercises 5-7, usethe following figure.Kelly is designing how she wants to put theplace settings for her party. She wants thetables to be set up symmetrically with thedesign that is on the table. First she placesplates as shown.

5. What is the order and magnitude of therotational symmetry of the figure?

6. Make the least possible number ofadditions of plates to the figure so thatthe table has rotational symmetry oforder 4 around its center.

7. Is it possible to rearrange the locationsof the 4 plates in the original figure sothat (1) their distance from the center ofthe table does not change, (2) theircenters remain somewhere on therectangle design, and (3) the resultingfigure has a rotational symmetry oforder 4? If so, draw the figure. If not,explain why.

M

9-3 Word Problem PracticeRotations

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1-48 Geo-09-873966 4/14/06 10:15 AM Page 26

Page 56: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 33 Glencoe Geometry

Less

on

9-4

9-4 Word Problem PracticeTessellations

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. DESIGN Henry drew a regulartessellation using congruent squares.Then, inside of each square he drewdiagonal lines connecting the vertices ofthe square to that square’s center.Describe the resulting tessellation.

2. BRICK WALLS Gordon wants to add abrick wall to his backyard. He wants touse rectangular bricks, but he does notwant to use them all in the sameorientation. Give an example of atessellation using 2 by 1 rectangles withsome oriented horizontally and someoriented vertically.

3. CIRCLES A tessellation cannot be madeusing congruent circles. However, it ispossible to tessellate the plane usingcircles together with other shapes. Showhow this can be done by using congruentcircles together with congruent copies ofone other shape.

4. TILES Show how to make a tessellationof tiles using the tile shape shown.

QUILTS For Exercises 5 and 6, use thefollowing information.Mona has been assigned a special mathproject that requires her to find an exampleof a tessellation in a real life situation. Sherecently completed a quilt using cloth piecesshaped liked decagons.

5. Is it possible the quilt is an example of atessellation?

6. Justify the solution to Exercise 5.

1-48 Geo-09-873966 4/14/06 10:21 AM Page 33

Page 57: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 40 Glencoe Geometry

9-5 Word Problem PracticeDilations

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. CENTERS Margot superimposed the image of the dilation of afigure on itsoriginalfigure asshown.Identify thecenter ofthis dilation.Explain how you can find it.

2. SCALE FACTORS Tyrone drew a shapetogether with one of its dilations on thesame coordinate plane as shown.

What is the scale factor of the dilation?

3. DILATIONS Cara is making images fora poster. She wants to thicken the fivepointed star shownby dilating it, andthen filling in thespace between theoriginal and itsimage. Sketch the dilated image withthe indicated center and a scale factor of 1.5.

4. COORDINATES Leila drew a polygonwith coordinates (-1, 2), (1, 2), (1, -2), and(-1, -2). She then dilated the image andobtained another polygon withcoordinates (6, 12), (6, -12), (-6, -12), and(-6, 12). What was the scale factor andcenter of this dilation?

FLOOR PLANS For Exercises 5 and 6,use the following information.Fred drew the floor plan of his house on acoordinate plane. He decided he wanted tomake it smaller because he wanted toinclude more.

5. Graph the image of Fred’s floor planafter a dilation centered at (0, 0) withscale factor 0.5.

6. The perimeter of the image is 26 units.What is the perimeter of the originalfigure?

y

xO

5

5-5

-5

y

xO

5

5-5

Image

Original figure

1-48 Geo-09-873966 4/14/06 10:25 AM Page 40

Page 58: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 9 47 Glencoe Geometry

Less

on

9-6

9-6 Word Problem PracticeVectors

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. WIND The vector v� represents thespeed and direction that the wind isblowing. Suddenly the wind picks upand doubles its speed, but the directiondoes not change. Write an expression fora vector that describes the new windvelocity in terms of v�

2. TRANSLATIONS Beth has a squarewith coordinates (–3, 2), (–4, 3), (–3, 4),and (–2, 3). She wants to move it toanother place using a translation by thevector v� = �7, –5�. What are thecoordinates of the image?

3. SWIMMING Jan is swimming in atriathlon event. When the ocean water isstill, her velocity can be represented bythe vector �2, 1� miles per hour. Duringthe competition, there was a fiercecurrent represented by the vector �–1, –1� miles per hour. What vectorrepresents Jan’s velocity during therace?

4. POLYGONS Draw a regular polygonaround the origin. For each side of thepolygon, associate a vector whosemagnitude is the length of thecorresponding side and whose directionpoints in the clockwise motion aroundthe origin. What vector represents thesum of all these vectors? Explain.

BASEBALL For Exercises 5 and 6, usethe following information.

Rick is in the middle of a baseball game. Histeammate throws him the ball, but throwsit far in front of him. He has to run as fastas he can to catch it. As he runs, he knowsthat as soon as he catches it, he has tothrow it as hard as he can to the teammateat home plate. He has no time to stop. Inthe figure, x� is the vector that representsthe velocity of the ball after Rick throws itand v� represents Rick’s velocity because heis running. Assume that Rick can throw justas hard when running as he can whenstanding still.

5. What vector would represent thevelocity of the ball if Rick threw it thesame way but he was standing still?

6. The angle between x� and v� is 89°. Byrunning, did it help Rick get the ball tohome plate faster than he would havenormally been able to if he werestanding still?

Homeplate

Rick

x

v

v�

x�

1-48 Geo-09-873966 4/14/06 10:39 AM Page 47

Page 59: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 10 10 Glencoe Geometry

10-1 Word Problem PracticeCircles and Circumference

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. WHEELS Zack is designing wheels for aconcept car. The diameter of the wheel is18 inches. Zack wants to make spokes inthe wheel that run from the center ofthe wheel to the rim. In other words,each spoke is a radius of the wheel. Howlong are these spokes?

2. CAKE CUTTING Kathy slices through acircular cake. The cake has a diameter of14 inches. The slice that Kathy made isstraight and has a length of 11 inches.

Did Kathy cut along a radius, adiameter, or a chord of the circle?

3. COINS Three identical circular coinsare lined up in a row as shown.

The distance between the centers of thefirst and third coins is 3.2 centimeters.What is the radius of one of these coins?

4. PLAZAS A rectangular plaza has asurrounding circular fence. Thediagonals of the rectangle pass from onepoint on the fence through the center ofthe circle to another point on the fence.

Based on the information in the figure,what is the diameter of the fence?Round your answer to the nearest tenthof a foot.

EXERCISE HOOPS For Exercises 5 and 6, use the following information.Taiga wants to make a circular loop that hecan twirl around his body for exercise. Hewill use a tube that is 2.5 meters long.

5. What will be the diameter of Taiga’sexercise hoop? Round your answer to thenearest thousandth of a meter.

6. What will be the radius of Taiga’sexercise hoop? Round your answer to thenearest thousandth of a meter.

377 ft

245 ft

3.2 cm

10 10 10

1-62 Geo-10-873967 5/16/06 10:05 AM Page 10

Page 60: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Less

on

10-

2

Chapter 10 17 Glencoe Geometry

1. CONDIMENTS A number of people in apark were asked to name their favoritecondiment for hot dogs. The results areshown in the circle graph.

What was the second most popular hotdog condiment?

2. CLOCKS Shiatsu is a Japanesemassage technique. One of the beliefs isthat various body functions are mostactive at various times during the day.To illustrate this, they use a Chineseclock that is based on a circle dividedinto 12 equal sections by radii.

What is the measure of any one of the12 equal central angles?

3. PIES Yolanda has divided a circularapple pie into 4 slices by cutting the piealong 4 radii. The central angles of the 4slices are 3x, 6x – 10, 4x + 10, and 5xdegrees. What exactly are the numericalmeasures of the central angles?

4. RIBBONS Cora is wrapping a ribbonaround a cylinder-shaped gift box. Thebox has a diameter of 15 inches and theribbon is 60 inches long. Cora is able towrap the ribbon all the way around thebox once, and then continue so that thesecond end of the ribbon passes the firstend. What is the central angle formedbetween the ends of the ribbon? Roundyour answer to the nearest tenth of a degree.

BIKE WHEELS For Exercises 5 and 6,use the following information.Lucy had to buy a new wheel for her bike.The bike wheel has a diameter of 20 inches.

5. If Lucy rolls the wheel one completerotation along the ground, how far willthe wheel travel? Round your answer tothe nearest hundredth of an inch.

6. If the bike wheel is rolled along theground so that it rotates 45°, how farwill the wheel travel? Round youranswer to the nearest hundredth of an inch.

7. If the bike wheel is rolled along theground for 10 inches, through whatangle does the wheel rotate? Round youranswer to the nearest tenth of a degree.

PC7pm-9pm

KID5pm-7pm

ST7am-9am

LI5am-7am

TW9pm-11pm

BL3pm-5pm

SP9am-11am

LU3am-5am

GB11pm-1am

SI1pm-3pm

HT11am-1pm

LIV1am-3am

Ketchup 198º

Mayonnaise 16.1ºOther 4.6º

Mustard111.9º Relish

29.4º

10-2 Word Problem PracticeMeasuring Angles and Arcs

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1-62 Geo-10-873967 4/19/06 10:28 AM Page 17

Page 61: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 10 24 Glencoe Geometry

10-3 Word Problem PracticeArcs and Chords

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. HEXAGON A hexagon is constructed asshown in the figure.

How many different chord lengths occuras side lengths of the hexagon?

2. FENCING A contractor is hired to builda fence around a circular park. Thecontractor traces out 10 radial lines eachseparated by 36°. He places a post whereeach line intersects the perimeter of thepark. He then connects consecutive postswith a straight fence. The result is afence that has the shape of a polygonwith 10 sides. Is this polygon a regulardecagon? Explain.

3. BIKE PATHS Carl is planning to visit acircular park. The radius of the park is 8miles. He is looking at a map of the parkand sees that the park has fivelandmarks along its edge. Thelandmarks are connected by paths ofequal length for biking. These pathsform a regular pentagon inscribed in thecircle. If Carl bikes along these paths tovisit each landmark, how many mileswill he bike?

4. CENTERS Neil wants to find the centerof a large circle drawn in the pavementof the schoolyard. He draws what hethinks is a diameter of the circle andthen marks its midpoint and declaresthat he has found the center. His teachercomes by and asks Neil how he knowsthat the line he drew is really thediameter of the circle and not a smallerchord. Neil realizes that he does notknow for sure. Explain what Neil can doto determine if it is an actual diameter.

A TALE OF TWO TRIANGLES ForExercises 5 and 6, use the followinginformation.An equilateral triangle is inscribed in acircle with center O. The triangle is thenrotated 30° to obtain another equilateraltriangle inscribed in the circle.

5. What is m�AOC?

6. Prove that the diameter through B isperpendicular to the diameter through C.

A B

CO

1-62 Geo-10-873967 4/19/06 10:33 AM Page 24

Page 62: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Less

on

10-

4

Chapter 10 31 Glencoe Geometry

10-4 Word Problem PracticeInscribed Angles

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. ARENA A circus arena is lit by fivelights equally spaced around theperimeter.

What is m�1?

2. FIELD OF VIEW The figure shows a topview of two people in front of a very tallrectangular wall. The wall makes achord of a circle that passes throughboth people.

Which person has more of theirhorizontal field of vision blocked by thewall?

3. RHOMBI Paul is interested incircumscribing a circle around arhombus that is not a square. He ishaving great difficulty doing so. Can youhelp him? Explain.

4. STREETS Three kilometers separate theintersections of Cross and Upton andCross and Hope.

What is the distance between theintersection of Upton and Hope and thepoint midway between the intersectionsof Upton and Cross and Cross andHope?

INSCRIBED HEXAGONS For Exercises 5and 6, use the following information.

You will prove that the sum of the measuresof alternate interior angles in an inscribedhexagon is 360.

5. How are �A and �BCF related?Similarly, how are �E and �DCFrelated?

6. Show that m�A + m �BCD + m�E =360°.

B

C

DE

F

A

Hope St.

Cross Ave.

Upto

n St

.

A

B

1

1-62 Geo-10-873967 4/20/06 2:05 PM Page 31

Page 63: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 10 38 Glencoe Geometry

10-5 Word Problem PracticeTangents

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. CANALS The concrete canal inLandtown is shaped like a “V” at thebottom. One day, Maureen accidentallydropped a cylindrical tube as she waswalking and it rolled to the bottom ofthe dried out concrete canal. The figureshows a cross section of the tube at thebottom of the canal.

Compare the lengths AV and BV.

2. PACKAGING Taylor packed a sphereinside a cubic box. He had painted thesides of the box black before putting thesphere inside. When the sphere waslater removed, he discovered that theblack paint had not completely dried andthere were black marks on the sides ofthe sphere at the points of tangencywith the sides of the box. If the blackmarks are used as the vertices of apolygon, what kind of polygon results?

3. TRIANGLES A circle is inscribed in a40°-60°-80° triangle. The points oftangency form the vertices of a triangleinscribed in the circle. What are theangles of the inscribed triangle?

4. ROLLING A wheel is rolling down anincline. Twelve evenly spaced diametersform spokes of the wheel.

When spoke 2 is vertical, which spokewill be perpendicular to the incline?

DESIGN For Exercises 5 and 6, use thefollowing information.Amanda wants to make this design ofcircles inside an equilateral triangle.

5. What is the radius of the large circle tothe nearest hundredth of an inch?

6. What are the radii of the smaller circlesto the nearest hundredth of an inch?

10 in6

60˚

1211

109 8 7

54

321

80˚

40˚ 60˚

A

V

B

1-62 Geo-10-873967 4/19/06 10:43 AM Page 38

Page 64: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Less

on

10-

6

Chapter 10 47 Glencoe Geometry

1. TELESCOPES Vanessa looked throughher telescope at a mountainouslandscape. The figure showswhat she saw.Based on the view,approximatelywhat angledoes the side ofthe mountainthat runs from A to B make with thehorizontal?

2. RADAR Two airplanes were tracked onradar. They followed the paths shown inthe figure.

What is the acute angle between theirflight paths?

3. EASELS Francisco is a painter. He places acircular canvas on hisA-frame easel andcarefully centers it.The apex of the easelis 30° and the measureof arc BC is 22°. Whatis the measure of arcAB?

4. FLYING When flying at an altitude of 5miles, the lines of sight to the horizonlooking north and south make about a173.7° angle. How much of the longitudeline directly under the plane is visiblefrom 5 miles high?

STAINED GLASS For Exercises 5 and 6,use the following information.Pablo made the stained glass windowshown. He used an inscribed square andequilateral triangle for the design.

5. Label the angle measures on the outeredge of the triangle.

6. Label all of the arcs with their degreemeasure.

55˚

173.7˚

A

B C

A

B

10-6 Word Problem PracticeSecants, Tangents, and Angle Measures

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1-62 Geo-10-873967 4/19/06 10:55 AM Page 47

Page 65: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 10 54 Glencoe Geometry

10-7 Word Problem PracticeSpecial Segments in a Circle

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. ICE SKATING Ted skated through oneof the face-off circles at a skating rink.His path through the circle is shown inthe figure.Given thatthe face-off circle is15 feet indiameter,whatdistancewithin theface-off circle did Ted travel?

2. HORIZONS Assume that Earth is aperfect sphere with a diameter of 7926miles. From analtitude of a miles,how long is thehorizon line h?

3. AXLES The figure shows the cross-section of an axle held in place by atriangular sleeve.A brake extendsfrom the apex ofthe triangle.When the brakeis extended 2.5inches into thesleeve, it comesinto contact withthe axle. What isthe diameter of the axle?

4. ARCHEOLOGY Scientists unearthedpart of a circular wall. They made themeasurements shown in the figure.

Based on the information in the figure,what was the radius of the circle?

PIZZA DELIVERY For Exercises 5 and 6,use the following information.Pizza Power is located at the intersection ofNorthern Boulevard and Highway 1 in acity with a circular highway running all theway around its outskirts. The radius of thecircular highway is 13 miles. Pizza Powerputs the map shown below on its take-outmenus.

5. How many miles away is the CircularHighway from Pizza Power if you travelnorth on Highway 1?

6. The city builds a new road along thediameter of Circular Highway thatpasses through the intersection ofNorthern Boulevard and Highway 1.Along this new road, about how manymiles is it (the shorter way) to theCircular Highway from Pizza Power?

Circular

Hig

h W

ay

2.8 mi

12.8 miNorthern Blvd.

22.4 mi

Highway 1

12 ft 12 ft

3 ft

4 in

2.5 in

7296mi

ah

Ted’s path

4 ft

5 ft

1-62 Geo-10-873967 4/19/06 11:00 AM Page 54

Page 66: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Less

on

10-

8

Chapter 10 61 Glencoe Geometry

10-8 Word Problem PracticeEquations of Circles

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. DESIGN Arthur wants to write theequation of a circle that is inscribed inthe square shown in the graph.

What is the equation of the desiredcircle?

2. DRAFTING The design for a park isdrawn on a coordinate graph. Theperimeter of the park is modeled by theequation (x – 3)2 + (x – 7)2 = 225. Eachunit on the graph represents 10 feet.What is the radius of the actual park?

3. WALLPAPER The design of a piece of wallpaper consists of circles that can be modeled by the equation (x – a)2 � (y – b)2 = 4, for all evenintegers b. Sketch part of the wallpaperon a grid.

4. SECURITY RING A circular safety ringsurrounds a top-secret laboratory. Onone map of the laboratory grounds, thesafety ring is given by the equation x2 +y2 – 20x + 14y = 175. Each unit on themap represents 1 mile. What is theradius of the safety ring?

DISTANCE For Exercises 5-7, use thefollowing information.Cleo lives the same distance from thelibrary, the post office, and her school. Thetable below gives the coordinates of theseplaces on a map with a coordinate gridwhere one unit represents one yard.

Location Coordinates

Library (–78, 202)

Post Office (111, 193)

School (202, –106)

5. What are the coordinates of Cleo’shome? Sketch the circle on a maplocating all three places and Cleo’shome.

6. How far is Cleo’s house from the placesmentioned?

7. Write an equation for the circle thatpasses through the library, post office,and school.

y

xO

5

5

1-62 Geo-10-873967 4/19/06 11:04 AM Page 61

Page 67: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 11 10 Glencoe Geometry

11-1 Word Problem PracticeAreas of Parallelograms

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. PACKAGING A box with a squareopening is squashed into the rhombusshown below.

What is the area of the opening?

2. RUNNING Jason jogs once around acity block shaped like a parallelogram.

How far did Jason jog?

3. SHADOWS A rectangular billboardcasts a shadow on the ground in theshape of a parallelogram. What is thearea of the groundcovered bytheshadow?Roundyouranswer tothe nearesttenth.

4. PATHS A concrete path shown below ismade by joining several parallelograms.

What is the total area of the path?

HIGHWAY SUPPORTS For Exercises 5and 6, use the following information.Four columns are being placed at thevertices of a parallelogram to support ahighway. Three of the columns are markedon the coordinate plane shown.

5. What are the coordinates of the threepossible locations of the fourth column?

6. What is the area in square units of eachof the three parallelograms that resultfrom the possibilities you found inExercise 5? Explain.

x

y

O-5 5

5

106” 144” 100” 128”

102 in

48” 48”

30 ft

15 ft

200 yd

100 yd

14 in

7 in

1-43 Geo-11-873968 4/19/06 11:49 AM Page 10

Page 68: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 11 19 Glencoe Geometry

Less

on

11-

2

1. INTERIOR DESIGN The 10 by 10square shows an office floor plancomposed of four congruent 8-sidedcubicles. What is the area of one of theseirregular 8-sided cubicles?

2. CUTOUTS Jeremy cut a rhombus out ofa 10-inch by 7-inch rectangle. Thediagonals of the rhombus are paralleland perpendicular to the sides of therectangle and are congruent to thelength and width of the rectangle,respectively.What is the totalarea of the fourshaded triangles?

3. SHARING Bernard has a piece of cakethat is shaped like a right triangle. Heneeds to cut it into three pieces to shareit with two friends. He divides one of thelegs into thirds and connects the divisionpoints to the oppositevertex of thetriangle asshown in thefigure.Which piece is the largest?

4. HEXAGONS Heather makes a hexagonby attaching two trapezoids together asshown. What is the area of the hexagon?

TILINGS For Exercises 5 and 6, use thefollowing information.Tile making often requires an artist to findclever ways of dividing a shape into severalsmaller, congruent shapes. Consider theisosceles trapezoid shown below.

5. Show how to divide the trapezoid into 3congruent triangles. What is the area ofeach triangle?

6. Show how to divide the trapezoid into 4congruent trapezoids. What is the areaof each of the smaller trapezoids?

1

2

60˚

0.5

60˚

1

260˚ 60˚

1

260˚ 60˚

20 cm

10 cm

15 cm

15 cm

30 cm

7 in

10 in

11-2 Word Problem PracticeAreas of Triangles, Trapezoids, and Rhombi

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1-43 Geo-11-873968 4/19/06 11:55 AM Page 19

Page 69: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 11 26 Glencoe Geometry

11-3 Word Problem PracticeAreas of Regular Polygons and Circles

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. LOBBY The lobby of a bank features alarge marble regular octagon. Each sideof the octagon is 15 feet long.

What is the area of the octagon? Roundyour answer to the nearest tenth.

2. PORTHOLES A circular window on aship has a radius of 8 inches. What isthe area of the window? Round youranswer to the nearest hundredth.

3. YIN-YANG SYMBOL A well-knownsymbol from Chinese culture is the yin-yang symbol, shown below.

Suppose the large circle has radius r, thesmall circles have radius �

8r

�, and the S-curve is two semicircles each withradius �

2r

�. In terms of r, what is the areaof the black region?

4. PYRAMIDS Martha’s clubhouse isshaped like a square pyramid with fourcongruent equilateral triangles for itssides. All of the edges are 6 feet long.What is the total surface area of theclubhouse including the floor? Roundyour answer to the nearest hundredth.

POOL DECKS For Exercises 5-7, use thefollowing information.Ricardo designs a square pool withsurrounding pool deck according to the planshown. The outer edge of the deck is aregular dodecagon with side length 20 feet.

5. What is the length of the apothem of thedodecagonal deck?

6. What is the length of the diagonal of thesquare pool?

7. What is the area of the deck?

20 ft

1-43 Geo-11-873968 4/19/06 11:59 AM Page 26

Page 70: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 11 33 Glencoe Geometry

Less

on

11-

4

11-4 Word Problem PracticeAreas of Composite Figures

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. FLOOR PLANS The floor plan of an L-shaped building is shown in thecoordinate plane. Each unit represents 5meters.

What is the area of the building?

2. DOG HOUSES Miranda is building adog house out of wood. The front view ofthe dog house is shown on thecoordinate plane below.

If each unit corresponds to 5 inches,what is the area of the front?

3. MINIATURE GOLF The plan for aminiature golf hole is shown below. Theright angle in the drawing is a centralangle.

What is the area of the playing surface?Round your answer to the nearesthundredth of a square meter.

4. TRACK A running track has an innerand outer edge. Both the inner and outeredge consists of two semicircles joined bytwo straight line segments. The straightline segments are 100 yards long. Theradii of the inner edge semicircles are 25yards and the radii of the outer edgesemicircles are 32 yards. What is thearea of the track? Round your answer tothe nearest hundredth of a yard.

SEMICIRCLES For Exercises 5 and 6,use the following information.Bridget arranged three semicircles in thepattern shown.

The right triangle has side lengths 6, 8, and10 inches.

5. What is the total area of the threesemicircles? Round your answer to thenearest hundredth of a square inch.

6. If the right triangle had side lengths �21�, �79�, and 10 inches, what wouldthe total area of the three semicirclesbe? Round your answer to the nearesthundredth of a square inch.

100 yd 25 yd

3 m

1.7 m

y

xO 5

5

y

xO 5

5

1-43 Geo-11-873968 4/19/06 12:04 PM Page 33

Page 71: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 11 40 Glencoe Geometry

11-5 Word Problem PracticeGeometric Probability and Areas of Sectors

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. DARTS A dart is thrown at thedartboard shown. Each sector has thesame central angle. The dart has equalprobability of hitting anypoint on thedartboard.What is theprobabilitythat the dartwill land in ashaded sector?

2. SPINNERS Jamie, Joe, and Patcelebrate the end of each work week byordering spring rolls from a Chineserestaurant. The order comes with 4spring rolls so somebody gets an extraroll. Because Jamie works full time andJoe and Pat work half time, they decidewho gets the extra roll by using aspinner that has a 50% chance of comingup Jamie, and 25% chances of coming upeither Joe or Pat. Design such a spinner.

3. RAIN A container has a square top witha hole as shown. What is the probabilitythat a raindrop that hits the containerfalls into the hole?Round your answerto the nearestthousandth.

4. ELECTRON MICROSCOPES Crystalplaces a 7 millimeter by 10 millimeterrectangular plate into the samplechamber of an electron microscope. Ablack and white checkerboard pattern of1-millimeter squares was painted overthe plate to identify different treatmentsof the material. When she turns on themonitor, she has no idea at what pointon the plate she is looking because thewhite and black contrast does not showup on the screen. If there are 2 moreblack squares than white squares, whatis the probability that she is looking at awhite square?

ENTERTAINMENT For Exercises 5 and 6, use the following information.A rectangular dance stage is lit by twolights that light up circular regions of thestage. The circles have the same radius and eachcircle passes through thecenter of the other. Thestage perfectlycircumscribes the two circles. A spectatorthrows a bouquet of flowers onto the stage.Assume the bouquet has an equal chance oflanding anywhere on the stage. (Hint: Useinscribed equilateral triangles.)

5. What is the probability that the flowersland on a lit part of the stage?

6. What is the probability that the flowersland on the part of the stage where thespotlights overlap?

14 in 7 in

1-43 Geo-11-873968 4/19/06 12:07 PM Page 40

Page 72: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 10 Glencoe Geometry

12-1 Word Problem PracticeRepresentations of Three-Dimensional Figures

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. LABELS Jamal removes the label froma cylindrical soup can to earn points forhis school. Sketch the shape of the label.

2. BLOCKS Margot’s three-year-old sonmade the magnetic block sculptureshown below in corner view.

Draw the right view of the sculpture.

3. CUBES Nathan marks the midpoints ofthree edges of a cube as shown.He then slicesthe cube along aplane thatcontains thesethree points.Describe theresulting cross section.

4. ENGINEERING Stephanie needs anobject whose top view is a circle andwhose left and front views are squares.Describe an object that will satisfy theseconditions.

DESK SUPPORTS For Exercises 5-7, usethe following information.The figure shows the support for a desk.

5. Draw the top view.

6. Draw the front view.

7. Draw the right view.

1 - 48 Geo-12-873969 4/20/06 9:56 AM Page 10

Page 73: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 18 Glencoe Geometry

12-2 Word Problem PracticeSurface Areas of Prisms

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. LOGOS The Z company specializes incaring for zebras. They want to make a3-dimensional “Z” to put in front of theircompany headquarters. The “Z” is 15inches thick and the perimeter of thebase is 390 inches.

What is the lateral surface area of this “Z”?

2. STAIRWELLS Management decides toenclose stairs connecting the first andsecond floors of a parking garage in astairwell shaped like an obliquerectangular prism.

What is the lateral surface area of thestairwell?

3. CAKES A cake is a rectangular prismwith height 4 inches and base 12 inchesby 15 inches. Wallace wants to applyfrosting to the sides and the top of thecake. What is the surface area of thepart of the cake that will have frosting?

4. CANDY A candy maker packages one ofits products in a triangular prism. Theheight of the prism is 10 inches. Thebase is an equilateral triangle with sidelength 3 inches. What is the surface areaof the package? Round your answer tothe nearest hundredth.

WOOD PLANKS For Exercises 5-8, usethe following information.A wood plank is a rectangular prism withlength 10 feet and base dimensions 2 inchesby 4 inches.

5. What is the surface area of the plank insquare inches?

6. Katrina cuts the plank in halflengthwise and obtains two wood planks,each 5 feet long. What is the totalsurface area of both planks?

7. If instead, Katrina had cut the plankinto N equal pieces lengthwise, whatwould be the total surface area of all Npieces?

8. Katrina wants to cut the plank into tworectangular pieces in a way that willgive her the greatest total surface areafor the pieces. How should she cut theplank?

16 ft

20 ft

15 ft

9 ft

15”

1 - 48 Geo-12-873969 4/20/06 10:03 AM Page 18

Page 74: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 25 Glencoe Geometry

Less

on

12-

3

12-3 Word Problem PracticeSurface Areas of Cylinders

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. DRUMS A drum is shaped like acylinder with a height of 5 inches and aradius of 7 inches. What is the surfacearea of the drum? Round your answer tothe nearest hundredth.

2. DRINKING GLASSES A drinking glassis shaped like a cylinder with a height of7 inches and a diameter of 3 inches.

What is the surface area of the drinkingglass? Remember that the glass has anopen top. Round your answer to thenearest hundredth.

3. ORIGAMI Hank takes a square sheetof paper and rolls it into a cylinder. Thesquare is 10 inches by 10 inches.

What are the dimensions of the cylinderand what is the lateral area of thecylinder? Round your answers to thenearest hundredth.

4. EXHAUST PIPES An exhaust pipe isshaped like a cylinder with a height of50 inches and a radius of 2 inches. Whatis the lateral surface area of the exhaustpipe? Round your answer to the nearesthundredth.

TOWERS For Exercises 5 and 6, use thefollowing information.A circular tower is made by placing onecylinder on top of another. Both cylindershave a height of 18 inches. The top cylinderhas a radius of 18 inches and the bottomcylinder has a radius of 36 inches.

5. What is the total surface area of thetower? Round your answer to thenearest hundredth.

6. Another tower is constructed by placingthe original tower on top of anothercylinder with a height of 18 inches and aradius of 54 inches. What is the totalsurface area of the new tower? Roundyour answer to the nearest hundredth.

18 in.

18 in.

1 - 48 Geo-12-873969 4/20/06 10:10 AM Page 25

Page 75: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 33 Glencoe Geometry

Less

on

12-

4

12-4 Word Problem PracticeSurface Areas of Pyramids

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. PAPER MODELS Patrick is making apaper model of a castle.Part of themodelinvolvescutting outthe netshown andfolding itinto apyramid. The pyramid has a squarebase. What is the lateral surface area ofthe resulting pyramid?

2. TETRAHEDRON Sung Li builds apaper model of a regular tetrahedron, apyramid with an equilateral triangle forthe base and three equilateral trianglesfor the lateral faces. One of the faces ofthe tetrahedron has an area of 17 squareinches. What is the total surface area ofthe tetrahedron?

3. PAPERWEIGHTS Daphne uses apaperweight shaped like a pyramid witha regular hexagon for a base. The sidelength of the regular hexagon is 1 inch.The altitude of the pyramid is 2 inches.

What is the lateral surface area of thispyramid? Round your answers to thenearest hundredth.

4. DICE A game needs random numbersbetween 1 and 8, inclusive. For thatreason, the game uses a die in the shapeof a regular octahedron. (A regularoctahedron can be made by attachingtwo square pyramids together alongtheir bases.) The lateral faces arecongruent equilateral triangles with sidelength 2 centimeters. What is thesurface area of the die?

Round your answer to the nearesthundredth.

CHEESE For Exercises 5 and 6, use thefollowing information.A piece of goat cheese is sold in the shape ofa square pyramid. The base has a sidelength of 4 inches and the altitude is 3inches. Round your answers to the nearesthundredth.

5. Caroline cuts off the tip of the cheese byslicing the pyramid along a planeparallel to the base resulting in asmaller square pyramid with an altitudeof 1 inch. What is the surface area ofthis cheese tip?

6. What is the surface area of theremaining part of the cheese?

20 cm20 cm15 cm

1 - 48 Geo-12-873969 4/20/06 10:15 AM Page 33

Page 76: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 40 Glencoe Geometry

12-5 Word Problem PracticeSurface Areas of Cones

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. HALF CIRCLES Charles cuts out asemicircle with a radius of 5 inches froma piece of paper. He then curls it into acone by joining the two radii on the edgeof the semicircle together.

What is the lateral surface area of theresulting cone? Round your answer tothe nearest hundredth.

2. CASTLES A right circular cone with analtitude of 20 feet and a radius of 6 feetserves as the highest cap of a castle.

What is the lateral surface area of thiscone? Round your answer to the nearesthundredth.

3. PAINTING Naomi is asked to paint anumber of congruent cones. She is toldthat the radius of the cones is 6 inchesand the altitude of the cones is 2 inches.What is the surface area of the cones?Round your answer to the nearesthundredth.

4. SPRAY PAINT A can of spray paintshoots out paint in a cone shaped mist.The lateral surface area of the cone is65π square inches when the can is held12 inches from a canvas. What is thearea of the part of the canvas that getssprayed with paint? Round your answerto the nearest hundredth.

MEGAPHONES For Exercises 5-7, usethe following information.A megaphone is formed by taking a conewith a radius of 20 centimeters and analtitude of 60 centimeters and cutting offthe tip. The cut is made along a plane thatis perpendicular to the axis of the cone andintersects the axis 12 centimeters from thevertex. Round your answer to the nearesthundredth.

5. What is the lateral surface area of theoriginal cone?

6. What is the lateral surface area of thetip that is removed?

7. What is the lateral surface area of themegaphone?

1 - 48 Geo-12-873969 4/20/06 10:42 AM Page 40

Page 77: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 12 47 Glencoe Geometry

Less

on

12-

6

12-6 Word Problem PracticeSurface Areas of Spheres

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. ORANGES Mandy cuts a sphericalorange in half along a great circle. If theradius of the orange is 2 inches, what isthe area of the cross section that Mandycut? Round your answer to the nearesthundredth.

2. COFFEE TABLES A coffee table is madeby taking a sphere with a radius of 26inches and then cutting it along twoparallel planes. The two planes are both10 inches from the center of the sphere.The section of the sphere that containsits center is used as the table.

What is the area of the tabletop?

3. MOONS OF SATURN The planetSaturn has several moons. These can bemodeled accurately by spheres. Saturn’slargest moon Titan has a radius of about2575 kilometers. What is theapproximate surface area of Titan?Round your answer to the nearest tenth.

4. METEORS A spherical meteorite lieshalf exposed in the earth. The diameterof the meteorite is 14 inches. What is thesurface area of the exposed surface?Round your answer to the nearesthundredth.

CUBES For Exercises 5-7, use thefollowing information.Marcus builds a spherical container for acube. The cube fits snugly inside the sphereso that the vertices of the cube touch theinside of the sphere. The side length of thecube is 2 inches.

5. What is the surface area of the cube?

6. What is the surface area of the sphere?Round your answers to the nearesthundredth.

7. What is the ratio of the surface area ofthe cube to the surface area of thesphere? Round your answer to thenearest hundredth.

1 - 48 Geo-12-873969 4/20/06 10:45 AM Page 47

Page 78: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 13 10 Glencoe Geometry

13-1 Word Problem PracticeVolumes of Prisms and Cylinders

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. TRASH CANS The Meyer family uses akitchen trash can shaped like a cylinder.It has a height of 18 inches and abase diameter of12 inches.

What is thevolume of thetrash can? Roundyour answer tothe nearest tenth of a cubic inch.

2. BENCH Inside a lobby, there is a pieceof furniture for sitting. The furniture isshaped like a simple block with a squarebase 6 feet on each side and a height of 1�

35

� feet.

What is the volume of the seat?

3. FRAMES Margaret makes a squareframe out of four pieces of wood. Eachpiece of wood is a rectangularprism with alength of 40centimeters, aheight of 4centimeters, anda depth of 6centimeters.What is the total volume of the woodused in the frame?

4. PENCIL GRIPS A pencil grip is shapedlike a triangular prism with a cylinderremoved from the middle. The base ofthe prism is a right isosceles trianglewith leg lengths of 2 centimeters. Thediameter of the base of the removedcylinder is 1 centimeter. The heights ofthe prism and the cylinder are the same,and equal to 4 centimeters.

What is the exact volume of the pencilgrip?

TUNNELS For Exercises 5 and 6, usethe following information.Construction workers are digging a tunnelthrough a mountain. The space inside thetunnel is going to be shaped like arectangular prism. The mouth of the tunnelwill be a rectangle 20 feet high and 50 feetwide and the length of the tunnel will be900 feet.

5. What will the volume of the tunnel be?

6. If instead of a rectangular shape, thetunnel had a semicircular shape with a50-foot diameter, what would be itsvolume? Round your answer to thenearest cubic foot.

6 ft6 ft

1 ft35

18 in

12 in

1-41 Geo-13-873970 4/20/06 11:11 AM Page 10

Page 79: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 13 17 Glencoe Geometry

Less

on

13-

2

1. ICE CREAM DISHES The part of a dishdesigned for ice cream is shaped like anupside-down cone. The base of the conehas a radius of 2 inches and the heightis 1.2 inches.

What is the volume of the cone? Roundyour answer to the nearest hundredth.

2. GREENHOUSES A greenhouse has theshape of a square pyramid. The base hasa side length of 30 yards. The height ofthe greenhouse is 18 yards.

What is the volume of the greenhouse?

3. TEEPEE Caitlyn made a teepee for aclass project. Her teepee had a diameterof 6 feet. The angle the side of the teepeemade with the ground was 65º.

What was the volume of the teepee?Round your answer to the nearesthundredth.

4. SCULPTING A sculptor wants to removestone from a cylindrical block 3 feet highand turn it into a cone. The diameter ofthe base of the cone and cylinder is 2feet.

What is the volume of the stone that thesculptor must remove? Round youranswer to the nearest hundredth.

STAGES For Exercises 5-7, use thefollowing information.A stage has the form of a square pyramidwith the top sliced off along a plane parallelto the base. The side length of the topsquare is 12 feet and the side length of thebottom square is 16 feet. The height of thestage is 3 feet.

5. What is the volume of the entire squarepyramid that the stage is part of?

6. What is the volume of the top of thepyramid that is removed to get thestage?

7. What is the volume of the stage?

12 feet

16 feet

3 feet

65˚

30 yd

18 yd

13-2 Word Problem PracticeVolumes of Pyramids and Cones

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1-41 Geo-13-873970 4/20/06 11:47 AM Page 17

Page 80: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 13 24 Glencoe Geometry

13-3 Word Problem PracticeVolumes of Spheres

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. BALLS Many sports use spherical balls.A regulation basketball is a sphere with adiameter of 9 inches. What is the volumeof this sphere? Round your answer to thenearest thousandth ofa cubic inch.

2. BILLIARDS A billiard ball set consistsof 16 spheres, each 2�

14

� inches indiameter. What is the total volume of acomplete set of billiard balls? Roundyour answer to the nearest thousandthof a cubic inch.

3. FRUIT A cantaloupe is a nearlyspherical fruit. Inside, there is a roughlyspherical cavity in the center that holdsseeds. The flesh surrounds this cavityand extends to the skin of the fruit. Theseed cavity is about half the radius ofthe fruit.

About what percentage of the cantaloupeis edible flesh?

4. THE ATMOSPHERE About 99% ofEarth’s atmosphere is contained in a 31-kilometer thick layer that enwrapsthe planet. The Earth itself is almost asphere with radius 6378 kilometers.What is the ratio of the volume of theatmosphere to the volume of Earth?Round your answer to the nearestthousandth.

GLASSES For Exercises 5 and 6, usethe following information.Jordan has two glasses. One is ahemisphere of radius 2 inches. The other isa cylinder with base radius 1�

14

� inches.

5. What is the volume of the hemisphericalglass? Round your answer to the nearestthousandth of a square inch.

6. If the cylindrical glass can hold twice asmuch water as the hemispherical glass,what is the height of the cylinder?Round your answer to the nearesthundredth of an inch.

1

2 in.

in.14

Skin Flesh

Seed Cavity

9 in.

1-41 Geo-13-873970 4/20/06 11:53 AM Page 24

Page 81: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 13 32 Glencoe Geometry

13-4 Word Problem PracticeCongruent and Similar Solids

NAME ______________________________________________ DATE ____________ PERIOD _____

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

1. AQUARIUMS Manuel has anaquarium that measures 16 inches high,12 inches deep, and 20 inches long.Abigail has an aquarium that measures25 inches long, 20 inches high, and 15inches deep. Are the two aquariumssimilar, congruent, or neither?

2. SIZES Earth’s diameter is about 3.75times the diameter of the Moon. Howmany times as large is Earth comparedto the Moon? Round your answer to thenearest hundredth.

3. MODELS An architecture firm built ascale model of a building. The scale ofthe model is 1 inch : 15 inches. The scalemodel has 3456 square inches of officefloor space. How many square feet ofoffice space will the actual buildinghave?

4. STORAGE A chemical company wantedto order one cylindrical storage tank 12feet high with a base diameter of 6 feet.However, because of various cost andshipping factors, the company found itmore economical to purchase severalcylindrical storage tanks that were only4 feet high with a base diameter of 2feet. How many of these smaller tanksmust the company purchase to be able tostore the volume equivalent of the singlelarge tank?

ICOSAHEDRA For Exercises 5-7, use thefollowing information.An icosahedron is a Platonic solid that has20 faces, 30 edges, and 12 vertices. All of thefaces of an icosahedron are equilateraltriangles. All icosahedra are similar to eachother. The figure shows two icosahedra thatdiffer by a scale factor of 5 : 3.

5. What is the ratio of the surface area ofthe larger icosahedron to the smallerone?

6. What is the ratio of the volume of thelarger icosahedron to the smaller one?

7. Suppose the surface area of the largericosahedron is 100 square feet. What isthe surface area of the smallericosahedron?

1-41 Geo-13-873970 4/20/06 12:11 PM Page 32

Page 82: Word Problem Practice - Yola - Mrs. Kim's Geometrymrskimgeo.yolasite.com/resources/Geometry Word Problmem Practice.… · Word Problem Practice Distance and Midpoints ... Lesson 1-3

Chapter 13 39 Glencoe Geometry

Less

on

13-

5

13-5 Word Problem PracticeCoordinates in Space

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. CUBES Martha needs to specify thecoordinates of the vertices of a cube for acomputer program. Five of the vertices arelocated at (0, 0, 0), (5, 0,0), (0, 5, 0), (5, 5, 0), and(0, 0, 5). What are thecoordinates of theremaining threevertices?

2. HIKING Jasmine is going to hike up tothe summit of a mountain. The summitis located 4 kilometers east, 2 kilometersnorth, and 2,375 meters above hercurrent location. How far away is shefrom the summit? Round your answer tothe nearest meter.

3. ENGINEERING A bridge is held up by anetwork of steel rods. In a 3-dimensionalmodel of the network, one of the rodshas endpoints located at (5, 8, �3) and(1, 4, 5). Another rod has one endpointlocated at (�5, �2, �6) and the otherendpoint at the midpoint of the first rod.What are the coordinates of thismidpoint?

4. REFLECTIONS Norman created a solidthat has a plane of symmetry. In otherwords, if the solid were to be reflected inthe plane of symmetry, it would lookunchanged. The coordinates of his solidwere (�5, 0, 0), (0, �1, 0), (0, 0, 1), (0, 0,�2), (0, 6, 0), and (5, 0, 0). Identify theplane of symmetry.

RECTANGULAR SOLIDS For Exercises 5-8, use the following information.An architectural plan involves a rectangularsolid. The coordinates of one vertex of thesolid are (1, 2, 1) and the coordinates of thevertex diagonally opposite are (3, 5, 4). Thesides of the solid are parallel orperpendicular to the various coordinateplanes. Each unit corresponds to 4 feet.

5. Determine the coordinates of all 8 of thesolid’s vertices.

6. Sketch a graph of the solid in a 3-dimensional coordinate system.

7. What are the dimensions of the solid?

8. What are the surface area and volume ofthe solid?

y

z

x

1-41 Geo-13-873970 4/20/06 12:17 PM Page 39