Geometry Week of May 18th - May 22th

Submission: Please submit all of *your assignments by uploading to the corresponding Microsoft Teams assignment.* Guided Notes: Attached to this page are guided notes for you to fill in for each of the respective lessons for the week. The guided notes are meant to go along with the examples from each lesson in the textbook similarly to how we would take notes in class. You do not need to submit these back to me but are encouraged to use them as a resource for yourself to refer back to. IXL: All students should have the IXL username and password but if there are any problems logging in please contact your teacher as soon as possible. Please make sure that you are completing the assigned section letter and number for each lesson . This is acting as your lesson practice for each of these lesson topics so I am expecting to see roughly a half hour of time spent on the IXL topic each day. Homework: The lessons homework is also expected to be completed within two days of the video lesson (example: Monday’s hw will be due on Wednesday, Thursday and Fridays HW will be due on Monday). You will be responsible for completing the homework assignment for that lesson and submitting it via email. The lesson Practice will be due the day after the assigned video lesson (example: Tuesday’s Lesson Practice will be due Wednesday) Grading: Homework assignments will be graded as either Non Accuracy or Accuracy Homework assignments. IXL and lesson practice will be graded as classwork/participation grade. ALL work must be shown, and each problem must be attempted in order to receive full credit. The points awarded to each assignment is indicated below. Note: Attached at the end is study guide 20. This study guide will be due before the accuracy assessment for next week and will not be due this week. Assignments: Monday: Watch video on Lesson 110 and Lesson Practice 110 (10 points) and Lesson 110 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Wednesday 5/20. Tuesday: Watch video on Investigation 11 and Investigation 11 Practice (10 points) Submit by 11:59 on Thursday 5/21 Wednesday: Study Guide 20 is due today (10 points) Submit by 11:59 on Wednesday 5/20 by 11:59 pm Thursday: Complete Accuracy assignment on Microsoft teams. The assignment is based off of study guide 20 (48 points) Submit by 11:59 on Tuesday 5/26 Friday: Watch video on Lesson 111 and Lesson Practice 111 (10 points) and Lesson 111 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Tuesday 5/26. Collaboration is not allowed. Collaboration - to work jointly with others or together especially in an intellectual endeavor. When collaboration takes place, all students must demonstrate understanding of the new material.

Name:________________________________________ Period:___________ Date:_________________

Lesson 110 – Scale Drawings and Maps

Scale_______________________________________________________________________________

Scale Drawing________________________________________________________________________

____________________________________________________________________________________

Scale Model__________________________________________________________________________

____________________________________________________________________________________

1. The White House is approximately 168 feet long and 85 feet wide. Draw a scale representation of the base of the building using a scale of 1 cm:30 ft. Give your answer to the nearest tenth.

2. The carbon atom, which is roughly spherical, has an atomic radius or 70 picometers. If a student models the carbon atom with a scale of 5 pm:1 cm, what is the radius of the model?

Name:________________________________________ Period:___________ Date:_________________

3. Adina lives 145 miles from Darren. On the map, the distance is represented as 2 centimeters. If, on the map, Carmen lives 3.5 centimeters from Darren and 4 centimeters from Adina, what is the actual distance that Carmen lives from Adina and Darren?

Darren

Adina

Carmen

Name_______________________ Class Period_________ Date__________

Lesson 110 Lesson Practice a. Make a scale drawing of the base of an apartment building that is 30 meters long and 15 meters wide. Use a scale of 1 m: .5cm. b. The Washington Monument is approximately 555.5 feet tall. If a scale drawing of the Washington Monument is 10 inches tall, what is the scale?

c. The planet Mercury has a diameter of 3031 miles. If a scale model is made with a ratio of 200 miles: 1 foot, what is the diameter of the model? Round your answer to the nearest tenth. d. On a map of the United States, San Antonio is 3.3 centimeters away from Dallas. They are actually 277 miles apart. If Oklahoma City is 2.4 centimeters away from Dallas on the same map, how far apart are the two cities? What is the scale of the map? Round your answer to the nearest whole number.

Name:_____________________________________ Period:______________ Date:_______________

Geometry Lesson 110 Practice

Mrs. Rogers

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. The height of a tower on a scale drawing is 14 centimeters. The scale is 2 cm:13 m. What is the actual height

of the tower?

a. 91 m c. 28 m

b. 182 m d. 364 m

____ 2. On the plans for a new house, the house is 14 inches wide by 28 inches long. If the house is going to be 35

feet wide, what will the length of the house be?

a. 87.5 ft c. 17.5 ft

b. 70 ft d. 21 ft

____ 3. A model of a pyramid has a square base with each side measuring 35 cm. The height of the model is 50 cm.

The height of the original pyramid is 14 m. What is the measurement of each side of the base of the original

pyramid?

a. 87.5 m c. 14 m

b. 9.8 m d. 125 m

____ 4. A new medical complex being built has a rectangular base. It is 450 ft long, 180 ft wide, and 60 ft tall. If the

architect’s scale model is 42 in. long, what are the width and height of the model?

a. 126 in. wide, 42 in. tall c. 8.4 in. wide, 2.8 in. tall

b. 42 in. wide, 14 in. tall d. 16.8 in. wide, 5.6 in. tall

____ 5. Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On

the map, Lisa measures the distance to be 2.5 inches. How many miles do they have to drive if the map scale

is 1 in.:55 mi?

a. 137.5 miles c. 192.5 miles

b. 22 miles d. mile

____ 6. The height of a tower on a scale drawing is 6 centimeters. The scale is 2 cm:31 m. What is the actual height of

the tower?

a. 186 m c. 12 m

b. 372 m d. 93 m

____ 7. On the plans for a new house, the house is 14 inches wide by 18 inches long. If the house is going to be 28

feet wide, what will the length of the house be?

a. 36 ft c. 21.8 ft

b. 24 ft d. 56 ft

____ 8. A model of a pyramid has a square base with each side measuring 25 cm. The height of the model is 50 cm.

The height of the original pyramid is 12 m. What is the measurement of each side of the base of the original

pyramid?

a. 104.2 m c. 12 m

b. 6 m d. 52.1 m

0.045

Name:_____________________________________ Period:______________ Date:_______________

____ 9. A new medical complex being built has a rectangular base. It is 300 ft long, 120 ft wide, and 70 ft tall. If the

architect’s scale model is 36 in. long, what are the width and height of the model?

a. 7.2 in. wide, 4.2 in. tall c. 61.7 in. wide, 36 in. tall

b. 14.4 in. wide, 8.4 in. tall d. 36 in. wide, 21 in. tall

____ 10. Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On

the map, Lisa measures the distance to be 2.5 inches. How many miles do they have to drive if the map scale

is 1 in.:50 mi?

a. 20 miles c. 0.05 mile

b. 125 miles d. 175 miles

____ 11. Add the vectors , , and .

a. c.

b. d.

____ 12. Solve the system of equations algebraically.

a. (2, 15) c. (–4, 7)

b. (7, 2) d. (2, 7)

Problem

13. A kitchen is 17 feet long and 10 feet wide. Draw a scale representation of the floor of the kitchen using a scale

of 1 cm : 3 ft. Give your answer to the nearest tenth.

14. Decompose the vector .

Name:_____________________________________ Period:______________ Date:_______________

Name:____________________________________ Period:___________ Date:________________

Investigation 11 – Golden Ratio

Golden Ratio - _____________________________________________________________________ _________________________________________________________________________________. _________________________________________________________________________________ 1. Suppose two numbers, a and b, are in the golden ratio. If a is the larger number and a = 1, what

is b, in simplified radical form?

2. Suppose c and d are in the golden ratio. If c is the larger number and c = √5, what is d in simplified radical form?

3. Suppose e and f are in the golden ratio. If f is the smaller number and f = 2, what is e in simplified radical form?

Name:____________________________________ Period:___________ Date:________________

Golden Rectangle – ____________________________________________________________________ ____________________________________________________________________________________.

Let ABCD be a golden rectangle with 𝐴𝐵

𝐵𝐶=

𝑏

ℎ= 𝛷, where b is the longer side of the rectangle.

4. Write a proportion relating b and h.

5. Suppose b = 2√5. What is the value of h in simplified radical form?

Golden Spiral - _______________________________________________________________________

6. Draw the next iteration of the pattern. The next square should continue to spiral outwards(clockwise), below the squares that have been already drawn.

7. Draw the next iteration. This time, the square should border the left side of your existing squares.

8. Draw one more iteration of the golden spiral.

CC

Name_______________________ Class Period_________ Date__________

Investigation 11 Lesson Practice The Fibonacci sequence is the infinite sequence of numbers beginning 1, 1, 2, 3, 5, … such that each term is the sum of the two previous terms.

a. Determine the first ten Fibonacci numbers. Then, determine the ratios 1

1,

2

1,

3

2… of each

consecutive pair of these numbers. Round your answer to four decimal places, where necessary b. Based on part a, state a hypothesis about the ratios of consecutive Fibonacci numbers.

c. Check your hypothesis by calculating ratios until the value is fixed for the first 5 decimal places. d. Explain how the squares in the golden rectangle are related to the Fibonacci sequence.

Name:________________________________________ Period:___________ Date:_________________

Lesson 111: Finding Distance and Midpoint in Three Dimensions

Distance Formula for Three Dimensions

1. Find the distance between M(5, 7, -3) and N(0, -3, 3).

2. Find the distance between C(0, 5, 2) and D(2, 0, 4).

Name:________________________________________ Period:___________ Date:_________________

Midpoint Formula in Three Dimensions

3. The endpoints of 𝑋𝑌̅̅ ̅̅ are X(9, 4, -2) and Y(-3, 6, -8). Find the midpoint.

4. Two people are climbing a mountain. In terms of each other’s positions, the first climber is 75

meters north, 25 meters west, and 18 meters higher than the second climber. What is the distance between the two climbers? Round to the nearest tenth.

Name_______________________ Class Period_________ Date__________

Lesson 111 Lesson Practice

a. Find the distance between R(0, 12, -2) and S(6, 8, -3)

b. Find the midpoint of F (22, 14, 9) and G(15, -8, -6)

c. Two people are skydiving from an airplane. Approximately how far apart are they at the

instant when the first person is 40 feet west, 25 feet north, and 300 feet below the plane, the

second person is 25 feet west, 10 feet north, and 250 feet below the plane? Round your answer

to the nearest tenth.

Name:________________________________________ Period:___________ Date:________________

Geometry Lesson 111 CP HW

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Which rectangle comes closest to being a golden rectangle?

a.

c.

b.

d.

____ 2. What value does the ratio of consecutive Fibonacci numbers approach as the terms in the sequence increase?

a.

c.

b.

d.

____ 3. The endpoints of are and . What is the midpoint of ?

a. (2.5, 2.5, –6.5) d. (–25, 21, 15)

b. (–12.5, 10.5, 7.5) e. None correct

c. (5, 5, –13)

____ 4. Find the height of a rectangular prism with a 12 in. by 16 in. base and a 22 in. diagonal. Round to the nearest

tenth.

72

45

cm

cm

90

45

cm

cm

81

45

cm

cm

63

45

cm

cm

Name:________________________________________ Period:___________ Date:________________

a. 84.0 in. c. 884.0 in.

b. 9.2 in. d. 29.7 in.

____ 5. Find the distance between the points (8, 0, 9) and (9, 3, 12). Round to the nearest tenth.

a. 2.2 units c. 4.4 units

b. 27.2 units d. 2.7 units

____ 6. A rectangular prism has length l, width w, and height h. Find the length of the diagonal from A to B in terms

of l, w, and h.

a.

c.

b.

d.

____ 7. Find if . Round your answer to the nearest hundredth.

a. c. b. d.

Problem

8. Suppose two numbers , a and b, are in the golden ratio to each other. If b is the smaller number and is equal to

8, what is a in simplified radical form?

12

16

22

A

B

l

w

h

C

Name:________________________________________ Period:___________ Date:________________

9. The first step in creating a golden spiral is to draw two small squares next to each other. How are the side

lengths of the other squares determined?

10. The endpoints of are and . Find the midpoint.

11. Find the distance between points and . Round your answer to the nearest tenth.

12. Find if .

13. Find the area of the annulus in the concentric circles shown below.

4 cm

11 cm

Name:________________________________________ Period:___________ Date:________________

14. Find the measure of in the triangle below. Round your answer to the nearest hundredth of a degree.

15. Add the two matrices below.

From the book: 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 17, 21, 24, 26, 28

A

B C

1317

14