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Vocabulary
Review
Chapter 1 2
Nets and Drawings for Visualizing Geometry 1-1
Identify each figure as two-dimensional or three-dimensional.
1. 2. 3.
Vocabulary Builder
polygon (noun) PAHL ih gahn
Definition A polygon is a two-dimensional fi gure with three or more sides, where each side meets exactly two other sides at their endpoints.
Main Idea: A polygon is a closed fi gure, so all sides meet. No sides cross each other.
Examples: Triangles, rectangles, pentagons, hexagons, and octagons are polygons.
Use Your Vocabulary
Underline the correct word(s) to complete each sentence.
4. A polygon is formed by two / three or more straight sides.
5. A circle is / is not a polygon.
6. A triangle / rectangle is a polygon with three sides.
7. The sides of a polygon are curved / straight .
8. Two / Three sides of polygon meet at the same point.
Cross out the figure(s) that are NOT polygons.
9.
C
B
A
E
D
10. M
L
N
P
Q
11.
V
W U
SR
XT
cchh other
polygon
three-dimensional two-dimensional three-dimensional
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Problem 1
BB
HSM11_GEMC_0101_T93725
E
A B C
F
D
3 Lesson 1-1
Underline the correct word(s) to complete the sentence.
12. A net is a two-dimensional / three-dimensional diagram that you can fold to form
a two-dimensional / three-dimensional figure.
13. Circle the net that you can NOT fold into a cube.
HSM11_GMSE_0101_14057
HSM11_GMSE_0101_14058
HSM11_GMSE_0101_14059
Use the net of a cube at the right for Exercises 14 and 15.
14. Suppose you fold the net into a cube. What number will be opposite each face?
1 3 4
15. Suppose you fold the net into a cube. What number is missing from each view?
?
15
HSM11_GMSE_0101_14061
HSM11_GMSE_0101_14062
?
2
3
HSM11_GMSE_0101_14063
?
6 4
Identifying a Solid From a Net
Got It? The net at the right folds into the cube shown. Which letters will be on the top and right side of the cube?
16. Four of the five other letters will touch some side of Face B when the net is folded into a cube. Cross out the letter of the side that will NOT touch some side of Face B.
A C D E F
17. Which side of the cube will that letter be on? Circle your answer.
Top Bottom Right Left Back
18. Use the net. Which face is to the right of Face B? How do you know?
_______________________________________________________________________
_______________________________________________________________________
19. Use the net. Which face is on the top of the cube? How do you know?
_______________________________________________________________________
_______________________________________________________________________
HSM11_GMSE_0101_14060
1
3 4
6
5
2
C. Explanations may vary. Sample: The left side of C and the right
side of B are the same edge of the cube.
E. Answers may vary. Sample: E folds down to become the top of
the cube.
6
4
5
1
2
3
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Problem 2
Problem 3
10 cm10 cm
7 cm4 cm
Chapter 1 4
Drawing a Net From a Solid
Got It? What is a net for the figure at the right? Label the net with its dimensions.
Write T for true or F for false.
20. Three of the faces are rectangles.
21. Four of the faces are triangles.
22. The figure has five faces in all.
23. Now write a description of the net.
_______________________________________________________________________
_______________________________________________________________________
24. Circle the net that represents the figure above.
10 cm
10 cm
4 cm
7 cm
10 cm
10 cm
4 cm
7 cm
7 cm
7 cm 7 cm
10 cm10 cm
10 cm
Isometric Drawing
Got It? What is an isometric drawing of this cube structure?
25. The cube structure has
edges that you can see and
vertices that you can see.
26. The isometric dot paper shows 2 vertices and 1 edge of the cube structure. Complete the isometric drawing.
Answers may vary. Sample: The net has three rectangles and two
triangles that fold to form the figure above.
T
F
T
24
16
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Math Success
Now Iget it!
Need toreview
0 2 4 6 8 10
Problem 4
Lesson Check
Right
Front
5 Lesson 1-1
Check off the vocabulary words that you understand.
net isometric drawing orthographic drawing
Rate how well you can use nets, isometric drawings, and orthographic drawings.
Orthographic Drawing
Got It? What is the orthographic drawing for this isometric drawing?
27. Underline the correct word to complete the sentence.
If you built the figure out of cubes, you would use seven / eight cubes
28. Cross out the drawing below that is NOT part of the orthographic drawing. Then label each remaining drawing. Write Front, Right, or Top.
Vocabulary Tell whether each drawing is isometric, orthographic, a net, or none.
29. Write dot paper, one view, three views or none. Then label each figure.
Top
Front Right
Right
Front
Do you UNDERSTAND?
top
one view
right
three views
cross out
dot paper
front
none
net orthographic isometric none
HSM11GEMC_0101.indd 5HSM11GEMC_0101.indd 5 3/1/09 1:29:33 PM3/1/09 1:29:33 PM
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Vocabulary
Review
Points, Lines, and Planes 1-2
Chapter 1 6
Draw a line from each net in Column A to the three-dimensional figure it represents in Column B.
Column A Column B
1.
2.
3.
Vocabulary Builder
conjecture (noun, verb) kun JEK chur
Main Idea: A conjecture is a guess or a prediction.
Definition: A conjecture is a conclusion reached by using inductive reasoning.
Use Your Vocabulary
Write noun or verb to identify how the word conjecture is used in each sentence.
4. You make a conjecture that your volleyball team will win.
5. Assuming that your sister ate the last cookie is a conjecture.
6. You conjecture that your town will build a swimming pool. verb
noun
noun
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d.Key Concept Undefined and Defined Terms
Postulates 11, 12, 13, and 14
Undefined or Defined Term Diagram Name
point A
P
line
plane
segment
ray
opposite rays
AB
AB
AB
CA, CB
7 Lesson 1-2
Write the correct word from the list on the right. Use each word only once.
7.
8.
9.
10.
11.
12.
Draw a line from each item in Column A to its description in Column B.
Column A Column B
13. plane HGE intersection of AB and line z
14. BF plane AEH
15. plane DAE line through points F and E
16. line y intersection of planes ABF and CGF
17. point A plane containing points E, F, and G
18. Complete each postulate with line, plane, or point.
Postulate 1-1 Th rough any two points there is exactly one 9.
Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one 9.
Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one 9.
Postulate 1-4 Th rough any three noncollinear points there is exactly one 9.
lineopposite rays
planepointray
segment
G
H
y
EF
D
A
B z
C
x
7 Lesson 1-2
line
point
line
plane
A
A
B
A BP
C
A B
A B
BCA
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d.Problem 3
Problem 2
A
E F
GB
CD
H
Chapter 1 8
Naming Segments and Rays
Got It? Reasoning EF) and FE
) form a line. Are they opposite rays? Explain.
For Exercises 2529, use the line below.
E F
25. Draw and label points E and F. Then draw EF) in one color and FE
) in another color.
26. Do EF) and FE
) share an endpoint? Yes / No
27. Do EF) and FE
) form a line? Yes / No
28. Are EF) and FE
) opposite rays? Yes / No
29. Explain your answer to Exercise 28.
_______________________________________________________________________
_______________________________________________________________________
Finding the Intersection of Two Planes
Got It? Each surface of the box at the right represents part of a plane. What are the names of two planes that intersect in
*BF)?
30. Circle the points that are on *BF) or in one of the two planes.
A B C D E F G H
31. Circle another name for plane BFG. Underline another name for plane BFE.
ABF BCD BCG CDH FGH
32. Now name two planes that intersect in *BF).
Write P if the statement describes a postulate or U if it describes an undefined term.
19. A point indicates a location and has no size.
20. Through any two points there is exactly one line.
21. A line is represented by a straight path that has no thickness and extends in two opposite directions without end.
22. If two distinct planes intersect, then they intersect in exactly one line.
23. If two distinct lines intersect, then they intersect in exactly one point.
24. Through any three nontcollinear points there is exactly one plane.
U
P
P
P
P
U
Answers may vary. Sample: The rays point in opposite directions
but they do not share an endpoint.
ABE, ABF, BFE, AFE, BFC, BFG, CBG, and CFG.
Answers may vary. Accept any variation of
HSM11GEMC_0102.indd 8HSM11GEMC_0102.indd 8 3/12/09 7:18:43 AM3/12/09 7:18:43 AM
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Lesson Check
Now Iget it!
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0 2 4 6 8 10
Math Success
Problem 4
MJ
N P
QRK
L
A B
9 Lesson 1-2
Do you UNDERSTAND?
Are AB) and BA
) the same ray? Explain.
Underline the correct symbol to complete each sentence.
36. The endpoint of AB) is A / B .
37. The endpoint of BA) is A / B .
38. Use the line. Draw and label points A and B. Then draw AB) and BA
).
39. Are AB) and BA
) the same ray? Explain.
_______________________________________________________________________
Check off the vocabulary words that you understand.
point line plane segment ray postulate axiom
Rate how well you understand points, lines, and planes.
Using Postulate 14
Got It? What plane contains points L, M, and N? Shade the plane.
33. Use the figure below. Draw LM , LN , and MN as dashed segments. Then shade plane LMN.
Underline the correct word to complete the sentence.
34. LM , LN , and MN form a triangle / rectangle .
35. Name the plane.
_______________________________________________________________________
M
J
N P
KR
Q
L
No. They point in opposite directions and have different endpoints.
Explanations may vary. Sample:
Answers may vary. Accept any of LMN, MNL, NLM, MLN, LNM, NML
HSM11GEMC_0102.indd 9HSM11GEMC_0102.indd 9 3/12/09 7:21:52 AM3/12/09 7:21:52 AM
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Vocabulary
Review
Chapter 1 10
1-3 Measuring Segments
Draw an example of each.
1. point 2. *AB) 3. DF
)
Vocabulary Builder
segment (noun) SEG munt
Definition: A segment is part of a line that consists of two endpoints and all points between them.
Main Idea: You name a segment by its endpoints.
Use Your Vocabulary
Complete each sentence with endpoint, endpoints, line, or points.
4. A ray has one 9.
5. A line contains infinitely many 9.
6. A segment has two 9.
7. A segment is part of a 9.
Place a check if the phrase describes a segment. Place an if it does not.
8. Earths equator
9. the right edge of a books cover 10. one side of a triangle
Every point on a line can be paired with a real number, called the coordinate of the point.
Postulate 15 Ruler Postulate
H J
segment HJ
endpoint
Answers may vary. Samples are shown.
points
endpoints
line
AA B D F
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d.Problem 1
Postulate 16 Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then AB 1 BC 5 AC .
Given points A, B, and C are collinear and B is between A and C, complete each equation.
13. AB5 5 and BC5 4, so AB1 BC 5 1 and AC 5 .
14. AC5 12 and BC5 7, so AC2 BC 5 2 and AB 5 .
Problem 2
J
4x 6 7x 15
K L
6 84 122 1626 0
VUS
4 10 14
11 Lesson 1-3
Measuring Segment Lengths
Got It? What are UV and SV on the number line?
11. Label each point on the number line with its coordinate.
12. Find UV and SV. Write a justification for each statement.
UV 5 P 2 P SV 5 P 2 P
UV 5 P P SV 5 P P
UV 5 SV 5
Using the Segment Addition Postulate
Got It? In the diagram, JL 5 120. What are JK and KL?
15. Write a justification for each statement.
JK 1 KL 5 JL
(4x 1 6) 1 (7x 1 15) 5 120
11x 1 21 5 120
11x 5 99
x 5 9
16. You know that JK 5 4x 1 6 and KL 5 7x 1 15. Use the value of x from Exercise 15 to to find JK and KL. Find JK and KL.
17. JK 5 and KL 5 .
24
24
4
14Definition of distance10 14
18
Subtract.
Find the absolute value.
218
5 4 9
12 7 5
Segment Addition Postulate
Simplify.
Subtract 21 from each side.
Divide each side by 11.
4(9) 1 6 5 36 1 6 5 42 and 7(9) 1 15 5 63 1 15 5 78
Substitute.
42 78
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Problem 3
A
6 4 2 0 2 4 6 8 10 12 14 16
B C D E
Chapter 1 12
Comparing Segment Lengths
Got It? Use the diagram below. Is AB congruent to DE?
In Exercises 18 and 19, circle the expression that completes the equation.
18. AB 5 j
22 2 2 u22 22 u u22 2 3 u u22 2 4 u
19. DE 5 j
3214 10114 u 5214 u u 10214 u
20. After simplifying, AB 5 and DE 5 .
21. Is AB congruent to DE? Explain.
_______________________________________________________________________
Th e midpoint of a segment is the point that divides the segment into two congruent segments.
Use the number line below for Exercises 2225.
42 31 53 25 4 0
JH IG KFEDCBA
1
22. Point is halfway between points B and J. 23. The midpoint of AE is point .
24. Point divides EK into two congruent segments.
25. Find the midpoint of each segment. Then write the coordinate of the midpoint.
AG DH AK
Midpoint
Coordinate
26. Find the coordinate of the midpoint of each segment.
segment with segment with endpoints at 24 and 2 endpoints at 22 and 4
Coordinate of midpoint
27. Circle the expression that relates the coordinate of the midpoint to the coordinates of the endpoints.
x11 x2
(x1 1 x2)2
(x1 2 x2)2
5 4
F
H
C
21 1
No. Segments with different lengths are not congruent.
Explanations may vary. Sample:
D F F
0022
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d.Problem 4
8x 11
T U V12x 1
Lesson Check
P Q R S T
2 3 4 5 6
Math Success
Now Iget it!
Need toreview
0 2 4 6 8 10
13 Lesson 1-3
Using the Midpoint
Got It? U is the midpoint of TV . What are TU, UV, and TV?
28. Use the justifications at the right to complete the steps below.
Step 1 Find x.
TU 5 UV Defi nition of midpoint
8x 1 11 5 Substitute.
8x 1 11 1 5 1 Add 1 to each side.
5 Subtract 8x from each side.
5 x Divide each side by 4.
Step 2 Find TU and UV.
TU 5 8 ? 1 11 5 Substitute for x.
UV 5 12 ? 2 1 5 Substitute.
Step 3 Find TV.
TV 5 TU 1 UV Defi nition of midpoint
5 1 Substitute.
5 Simplify.
Do you UNDERSTAND?
Vocabulary Name two segment bisectors of PR.
Underline the correct word or symbol to complete each sentence.
29. A bisector / midpoint may be a point, line, ray, or segment.
30. The midpoint of PR is point P / Q / R .
31. Line passes through point P / Q / R .
32. Two bisectors of PR are and .
Check off the vocabulary words that you understand.
congruent segments coordinate midpoint segment bisector
Rate how well you can fi nd lengths of segments.
12x2 1
1 1
12 4x
3
3 3
3 35
35 35
70
WV ? Why or why not?
_______________________________________________________________________
Draw a line from each word in Column A to the angles it describes in Column B.
Column A Column B
10. supplementary /1 and /2
11. adjacent /2 and /3
12. vertical /2 and /5
13. complementary /3 and /6
FC)
FD)
Congruence marks are on TW and WV .
Explanations may vary. Sample:
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d.
Problem 4
Problem 3
Postulate 19 Linear Pair Postulate
PK
(2x 24) (4x 36)
J
L
Overmatter
Chapter 1 20
Finding Missing Angle Measures
Got It? Reasoning lKPL and lJPL are a linear pair, mlKPL 5 2x 1 24, and mlJPL 5 4x 1 36. How can you check that mlKPL 5 64 and mlJPL 5 116?
22. What is one way to check solutions? Place a in the box if the response is correct. Place an in the box if it is incorrect.
Draw a diagram. If it looks good, the solutions are correct.
Substitute the solutions in the original problem statement.
23. Use your answer(s) to Exercise 22 to check the solutions.
24. How does your check show that you found the correct angle measurements?
_______________________________________________________________________
_______________________________________________________________________
Using an Angle Bisector to Find Angle Measures
Got It? KM) bisects lJKL. If mlJKL 5 72, what is mlJKM ?
25. Write a justification for each step.
m/JKM 5 m/MKL
m/JKM 1 m/MKL 5 m/JKL
2m/JKM 5 m/JKL
m/JKM 5 12 m/JKL
If two angles form a linear pair, then they are supplementary.
21. If /A and /B form a linear pair, then m/A 1 m/B 5 .180
mlKPL 5 642x 1 24 5 64 2x 5 40 x 5 20
ml JPL 5 1164x 1 36 5 116 4x 5 80 x 5 20
Answers may vary. Sample: You solved correctly because you found
the same solution to both equations.
Definition of angle bisector
Angle Addition Postulate
Substitute.
Divide each side by 2.
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Lesson Check
Now Iget it!
Need toreview
0 2 4 6 8 10
Math Success
L
M
K
36
36
J
4x
2x4x + 2x = 180
6x = 180x = 30
21 Lesson 1-5
Do you UNDERSTAND?
Error Analysis Your friend calculated the value of x below. What is her error?
28. Circle the best description of the largest angle in the figure.
acute obtuse right straight
29. Complete: 4x 1 2x 5
30. What is your friends error? Explain.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
Check off the vocabulary words that you understand.
angle complementary supplementary angle bisector vertical
Rate how well you can fi nd missing angle measures.
26. Complete.
m/JKL 5 , so m/JKM 5 .
27. Now complete the diagram below.
72 36
90
Answers may vary. Sample: She thought a right angle measures 1808,
so she set the sum of the angle measures equal to 180.
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Vocabulary
Review
S
G
W
P
W
s
s
Basic Constructions 1-6
Chapter 1 22
Draw a line from each word in Column A to its symbol or picture in Column B.
Column A Column B
1. congruent
2. point
3. ray
4. vertex
5. intersection of segments O
Vocabulary Builder
perpendicular (adjective) pur pun DIK yoo lur
Definition: Perpendicular means at right angles to a given line or plane.
Example: Each corner of this paper is formed by perpendicular edges of the page.
Non-Examples: Acute, obtuse, and straight angles do not have perpendicular rays.
Use Your Vocabulary
6. Circle the figure that shows perpendicular segments.
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d.Problem 1
Problem 2
X
Y
R S
B
Step 4 Open the ? to the length ofAC. With the compass point on pointS, draw an ? . Label where this arcintersects the other arc as point T.
compass / arc
Step 6 Draw FR.
Step 1 Use a straightedge to constructa ray with endpoint F.
Step 3 Use the same compasssetting. Put the ? point on pointF. Draw a long ? and label itsintersection with the ray as S.
compass / arc
Step 5 Use the same compass setting.Put the ? point on point T. Draw an ? and label its intersection with the first ? as point R.
compass / arc / arc
Step 2 With your ? point on vertex B,draw a(n) ? that intersects both sides of B. Label the points of intersection A and C.
compass / arc
B
A
C
RT
SF
23 Lesson 1-6
Constructing Congruent Segments
Got It? Use a straightedge to draw XY . Then construct RS so that RS 5 2XY.
7. A student did the construction at the right. Describe each
step of the construction.
Step 1
Step 2
Step 3
Step 4
Step 5
Constructing Congruent Angles
Got It? Construct lF so that mlF 5 2mlB at the right.
8. Use arc or compass to complete the sentence(s) in each step. In the large box, construct /F .
Use a straightedge to draw XY .
Draw a ray with endpoint R.
Draw an arc with compass point
Draw another arc with the compass point at the intersection.
Label the point of intersection S.
at R and opening XY.
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d.
Problem 3
S T
S M T
Y
X
Chapter 1 24
A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint.
9. Circle the drawing that shows the perpendicular bisector of a segment.
A
E
FB
A
E
F B
A
E
FB
Constructing the Perpendicular Bisector
Got It? Draw ST . Construct its perpendicular bisector.
10. Error Analysis A students construction of the perpendicular bisector of ST is shown below. Describe the students error.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
11. Do the construction correctly in the box below.
Answers may vary. Sample: The student did not make the opening
of the arc drawn from points S and T greater than 12ST.
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Need toreview
0 2 4 6 8 10
Math Success
Problem 4
Step 1 Put the compass point on vertex . Draw an arcthat intersects the sides of . Label the points of
intersection A and B.
Step 3 Draw .
Y
YP
Y
Step 2 Put the compass point on point A and draw an arc. With the same / a different
compass setting, draw an arc using point B. Be sure the arcs intersect. Label the point where the two arcs intersect P.
ZBY
X
A
P
25 Lesson 1-6
Do you UNDERSTAND?
Vocabulary What two tools do you use to make constructions?
Draw a line from each task in Column A to the tool used in Column B.
Column A Column B
13. measure lines compass
14. measure angles protractor
15. construct arcs ruler
16. construct lines straightedge
Check off the vocabulary words that you understand.
straightedge compass construction perpendicular bisector
Rate how well you can construct angles and bisectors.
Constructing the Angle Bisector
Got It? Draw obtuse lXYZ . Then construct its bisector YP).
12. Obtuse /XYZ is drawn in the box at the right. Complete the flowchart and do each step of the construction.
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Vocabulary
Review
x
y
O 4
4
24
4
B
A
C
G
DE
F
C
E F A
DB
x
y
8
510
Chapter 1 26
Midpoint and Distance in the Coordinate Plane1-7
Use the figure at the right for Exercises 16. Write T for true or F for false.
1. Points A and B are both at the origin.
2. If AB 5 BC , then B is the midpoint of AC .
3. The midpoint of AE is F.
4. The Pythagorean Theorem can be used for any triangle.
5. Point C is at (6, 0).
6. Point E has a y-coordinate of 28.
Vocabulary Builder
midpoint (noun) MID poynt
Definition: A midpoint of a segment is a point that divides the segment into two congruent segments.
Use Your Vocabulary
Use the figure at the right for Exercises 79.
7. The midpoint of EF is G( , ).
8. The midpoint of AB is ( , ), or the origin.
9. The midpoint of CD is ( , ).
F
F
F
T
F
F
0
0
0.5
0
2.5
0
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d.Key Concept Midpoint Formulas
Problem 2
2 4 6 8 10 12 14 16
2
4
(1, 2)
(17, 4)
( 4) 2
(1 ) 2
( , )
172
9 3
x
y
O
On a Number Line In the Coordinate Plane
Given A(x1, y1) and B(x2, y2), the coordinates of the
( ,x1 x22 )y1 y2
2midpoint of AB are M
The coordinate of the midpoint M of AB
.a b
2with endpoints at a and b is
Midpoint Formula Midpoint Coordinates
,( )4 9x1 1 3
2
y1 1 5
2,
9y1 1 5
25
18y1 1 5 5
13y1 5
4x1 1 3
25
8x1 1 3 5
11x1 5
Solve two equations.
( , )
Endpoint A Coordinates
3 5 ( )
27 Lesson 1-7
Finding an Endpoint
Got It? The midpoint of AB has coordinates (4, 29). Endpoint A has coordinates (23, 25). What are the coordinates of B?
15. Complete the equations below.
16. The coordinates of endpoint B are ( ).
Find the coordinate of the midpoint M of each segment with the given endpoints on a number line.
10. endpoints 5 and 9 11. endpoints 23 and 5
12. endpoints 210 and 23 13. endpoints 28 and 21
14. Complete the diagram below.
11, 13
7
26 12 24 12
1
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Problem 3
y2
y1
y2 y1
x1
x2 x1
x2O
y
x
d
B
A
a 2 b 2 c 2a
bc
y
8 4
4
8
53 2 (22) 5
x
6
1521 2 14 5
S(2, 14)
R(3, 1)
Chapter 1 28
Finding Distance
Got It? SR has endpoints S(22, 14) and R(3, 21). What is SR to the nearest tenth?
20. Complete the diagram at the right.
21. Let S(22, 14) be (x1, y1) and let R(3, 21) be (x2, y2) . Use the justifications and complete thesteps below to find SR.
d 5 Q 2 x1R2 1 Q 2 y1R2 Use the Distance Formula.
SR 5 Q 2 (22)R2 1 Q 2 14R2 Substitute.
5 Q R2 1 Q R2 Subtract.
5 1 Simplify powers.
5 Add.
< Use a calculator.
Formula The Distance Formula
Use the diagrams above. Draw a line from each triangle side in Column A to the corresponding triangle side in Column B.
Column A Column B
17. y2 2 y1 a
18. x2 2 x1 b
19. distance, d c
Th e distance between two points A(x1, y1) and B(x2, y2) is d 5 "(x2 2 x1)2 1 (y2 2 y1)2.Th e Distance Formula is based on the Pythagorean Th eorem.
y2
1
15
x2
3
5
25 225
250
15.8
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d.Problem 4
Math Success
Lesson Check
Now Iget it!
Need toreview
0 2 4 6 8 10
x
y
O103050 10
10
10
20
20
20 30 40 50
B
CA
D
E
F
x
y
O103050 10
10
10
20
20
20 30 40 50
B
CA
D
E
F
00000AAAAA 2222222000222002020202020222222202020
BBBBBBBBBBBB
AAAAAAAAFFFFFFF
OOOOOOOOOOOOOOOOO000000000000011111000000000000333333333 001
10000
10101000010000010000010000000000000
202020202000200000000000
2002000200
000000222 033 0400444444
CCCCCCCC
EEEEEEEEEEEEEEEEEEE
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO10000000000000000111111111113000000000000000033333333333333 100011
11111110010101010101010101010101
111011010110100101000100100101010101000101010101010101010000001000000101010
2202220202202020020202022020220200220020202020202020222022002020202020
220202020000202020
2000000000000000222222222222222 303003333 4040444404000044444444444444444444
BBBBBBBBBBBBBBB
CCCCCCCCCCCCCCCCCCCCCC
EEEEEEEEEEEEEEEE
111111
4444
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
AAACCCCCCCCCCCCCCCCCCCCC
DDDDDDDDDDDDDDDDDD
FFFFFFFFFFFFFFFF
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
29 Lesson 1-7
Finding Distance
Got It? On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform A and zip to each of the other platforms. How far do you travel from Platform D to Platform E? Each grid unit represents 5 m.
22. The equation is solved below. Write a justification for each step.
d 5 "(x2 2 x1)2 1 (y2 2 y1)2
DE 5 "(30 2 20)2 1 (215 2 20)2
5 "102 1 (235)2 5 "100 1 1225 5 "1325
23. To the nearest tenth, you travel about m.
Reasoning How does the Distance Formula ensure that the distance between two diff erent points is positive?
24. A radical symbol with no sign in front of it indicates a positive / negative square root.
25. Now answer the question.
__________________________________________________________________________________
Do you UNDERSTAND?
Check off the vocabulary words that you understand.
midpoint distance coordinate plane
Rate how well you can use the Midpoint and Distance Formulas.
Use the Distance Formula.
Sample: The radical in the Distance Formula represents a positive square root.
Substitute.
Simplify.
36.4
Answers may vary.
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Vocabulary
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Chapter 1 30
Perimeter, Circumference, and Area1-8
1. Cross out the shapes that are NOT polygons.
2. Write the name of each figure. Use each word once.
triangle square rectangle circle
Vocabulary Builder
consecutive (adjective) kun SEK yoo tiv
Definition: Consecutive means following in order without interruption.
Related Word: sequence
Example: The numbers 2, 4, 6, 8, . . . are consecutive even numbers.
Non-Example: The numbers 1, 3, 2, 5, 4, . . . are NOT consecutive numbers.
Use Your Vocabulary
Draw a line from each sequence of letters in Column A to the next consecutive letter in Column B.
Column A Column B
3. L, M, N, O, . . . R
4. V, U, T, S, . . . I
5. A, C, E, G. P
circle rectangle square triangle
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Problem 1
Problem 2
Key Concept Perimeter, Circumference, and Area
s
s
a c
b
hh
b
C r
d
24 m
c = dc = (24)c = 24
31 Lesson 1-8
Finding the Perimeter of a Rectangle
Got It? You want to frame a picture that is 5 in. by 7 in. with a 1-in.-wide frame. What is the perimeter of the picture?
7. The picture is in. by in.
8. Circle the formula that gives the perimeter of the picture.
P 5 4s P 5 2b 1 2h P 5 a 1 b 1 c C 5 pd
9. Solve using substitution.
10. The perimeter of the picture is in.
Finding Circumference
Got It? What is the circumference of a circle with radius 24 m in terms of ?
11. Error Analysis At the right is one students solution. What error did the student make?
_________________________________________________________
_________________________________________________________
12. Find the correct circumference.
6. Label the parts of each of the figures below.
Square Triangle Rectangle Circle
P 5 4s P 5 a 1 b 1 c P 5 2b 1 2h C 5 pd or C 5 2pr
A 5 s2 A 5 12bh A 5 bh A 5 pr2
5 7
24
P 5 2b 1 2h 5 2(5) 1 2(7) 5 10 1 14 5 24
C 5 2pr 5 2p(24) 5 48p
Answers may vary. Sample: The student used a diameter
of 24 m instead of a radius of 24 m.
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Problem 5
Problem 3
x
y
O 54321
2
3
4
5
12345
2
3
4
5
L
J
1M
K
7 ft
14 ft
Key Concept Postulate 110 Area Addition Postulate
Chapter 1 32
Finding Perimeter in the Coordinate Plane
Got It? Graph quadrilateral JKLM with vertices J(23, 23), K(1, 23), L(1, 4), and M(23, 1). What is the perimeter of JLKM?
13. Graph the quadrilateral on the coordinate plane at the right.
14. Use the justifications at the right to find the length of each side.
JK 5 P23 2 1 P Use the Ruler Postulate. 5 Simplify.
KL5 P 42 P Use the Ruler Postulate. 5 Simplify.
JM5 P 232 P Use the Ruler Postulate. 5 Simplify.
ML 5 (1 2 (23))2 1 (4 2 )2 Use the Distance Formula.
5 ( )
2 1 32 Simplify within parentheses.
5 ( ) 1 ( ) Simplify powers.
5 ( ) Add.
5 Take the square root.
15. Add the side lengths to find the perimeter.
JK 1 KL 1 JM 1 ML5 1 1 1 5
16. The perimeter of JKLM is units.
Finding Area of a Circle
Got It? The diameter of a circle is 14 ft. What is its area in terms of p?
17. Label the diameter and radius of the circle at the right.
18. Use the formula A 5 pr2 to find the area of the circle in terms of p.
19. The area of the circle is p ft2.
20. The area of a region is the sum / difference of the areas of its nonoverlapping parts.
4
4
4 4
16
25
20
20
5
49
5
9
4
7
7
1
1
23
A 5 pr2
5 p(7)2
5 49p
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Lesson Check
Now Iget it!
Need toreview
0 2 4 6 8 10
Math Success
Problem 6
9 cm
3 cm
3 cm
3 cm
6 cm
A1
A2
A3
3 cm
3 cm
9 cm
3 cm
9 cm
A1
A2A3
3 cm
9 cm A1 A1
A1
33 Lesson 1-8
Do you UNDERSTAND?
Compare and Contrast Your friend cant remember whether 2pr computes the circumference or the area of a circle. How would you help your friend? Explain.
22. Underline the correct word(s) to complete each sentence.
Area involves units / square units .
Circumference involves units / square units .
The formula 2pr relates to area / circumference because it involves units / square units .
Check off the vocabulary words that you understand.
perimeter area
Rate how well you can fi nd the area of irregular shapes.
Finding Area of an Irregular Shape
Got It? Reasoning The figure below shows one way to separate the figure at the left. What is another way to separate the figure?
21. Draw segments to show two different ways to separate the figure. Separate the left-hand figure into three squares. Drawings will vary. Samples are given.
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