Download Chapter Review 7

Chapter Review
CHAPTER
7
7-1 Angle Relationships
Use the diagram to name each geometric figure.
Q
R
70°
P
90°
T
20°
S
1. two obtuse angles
2. two acute angles
In the figure, ⬔1 and ⬔3 are vertical angles, and ⬔2 and ⬔4 are vertical
angles.
3. If m⬔2 ⫽ 100°, find m⬔1.
1 2
4 3
4. If m⬔2 ⫽ 100°, find m⬔4.
7-2 Parallel and Perpendicular Lines
c
In the figure, line a 冷冷 line b.
1
2
3
a
4
5
6
7
5. Name all angles congruent to ⬔6.
b
8
6. Name all angles congruent to ⬔8.
7. Which line is the transversal?
8. Name three pairs of supplementary angles.
7-3 Triangles
Find the value of each variable.
9.
10.
31°
11.
w°
y°
2w°
x°
Copyright © by Holt McDougal.
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30°
(3y + 10)°
31°
161
Holt McDougal Mathematics
CHAPTER 7 REVIEW CONTINUED
7-4 Polygons
Find the sum of the angle measures of each polygon. Then, if the polygon
is regular, find the measure of each angle.
12. 14-gon
13. 13-gon
14. octagon
Find the value of each variable.
15.
120°
x°
50°
130°
16.
105°
17.
145°
90°
32°
162°
122°
95°
y°
w°
77°
105°
7-5 Coordinate Geometry
Find the coordinates of the midpoint of each segment.
18.
19.
y
A
4
3
2
1
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
y
Y
x
4
3
2
1
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
X
1 2 3 4
B
x
1 2 3 4
7-6 Congruence
Z
Write a congruence statement for each pair of polygons.
20.
21.
F
H
36°
121°
D
E
121°
62°
Q
58°
I
23°
120°
P
G
120° W
R
60°
120° X
S
Y
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Holt McDougal Mathematics
CHAPTER 7 REVIEW CONTINUED
7-7 Transformations
22. Graph a reflection across
the x-axis.
y
y
B
4
3
2
1
A
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
4
3
2
1
C
x
x
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
1 2 3 4
4
3
2
1
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
B
A
y
B
A
23. Graph a rotation 90° clockwise
about the origin.
2 3 4
D
C
y
4
3
2
1
C
x
x
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
1 2 3 4
ⴚ2
ⴚ3
ⴚ4
B
A
2 3 4
D
C
7-8 Symmetry
Complete each figure. The dashed line is the line of symmetry.
24.
25.
26.
Complete each figure. The point is the center of rotation.
27. 4-fold
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28. 2-fold
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Holt McDougal Mathematics
CHAPTER
Big Ideas
7
Answer these questions to summarize the important concepts from
Chapter 7 in your own words.
1. Explain the difference between complementary angles and supplementary
angles.
2. If ⬔1 is 50°, explain how to find m⬔5.
2 1
3 4
5 6
7 8
3. If the measures of two angles in a triangle are 43° and 74°, explain how to
find the measure of the third angle.
4. Explain how to rotate a figure with vertices A(–1, 5), B(4, 5), C(4, –2), and
D(–1, –2) 90° counterclockwise about the origin. Give the coordinates of
the image.
For more review of Chapter 7:
• Complete the Chapter 7 Study Guide and Review on pages 380–382 of
your textbook.
• Complete the Ready to Go On quizzes on pages 358 and 376 of your
textbook.
Copyright © by Holt McDougal.
All rights reserved.
164
Holt McDougal Mathematics
Chapter Review
CHAPTER
7
7-1 Angle Relationships
Use the diagram to name each geometric figure.
Q
R
70°
P
90°
T
20°
S
1. two obtuse angles
2. two acute angles
⬔QTS, ⬔PTR
⬔PTQ, ⬔RTS
In the figure, ⬔1 and ⬔3 are vertical angles, and ⬔2 and ⬔4 are vertical
angles.
3. If m⬔2 100°, find m⬔1.
m⬔1 80°
4. If m⬔2 100°, find m⬔4.
m⬔4 100°
1 2
4 3
7-2 Parallel and Perpendicular Lines
c
In the figure, line a line b.
1
5. Name all angles congruent to ⬔6.
⬔2, ⬔3, ⬔7
6. Name all angles congruent to ⬔8.
⬔1, ⬔4, ⬔5
7. Which line is the transversal?
2
3
a
4
5
6
7
b
8
line c
8. Name three pairs of supplementary angles.
7-3 Triangles
Possible answers: ⬔1 and ⬔2,
⬔1 and ⬔3, ⬔3 and ⬔4
Find the value of each variable.
9.
10.
31°
11.
w°
y°
2w°
x°
x 118°
Copyright © by Holt McDougal.
All rights reserved.
(3y + 10)°
30°
31°
w 30°
y 35°
161
Holt McDougal Mathematics
CHAPTER 7 REVIEW CONTINUED
7-4 Polygons
Find the sum of the angle measures of each polygon. Then, if the polygon
is regular, find the measure of each angle.
12. 14-gon
13. 13-gon
2160°; 154.3°
14. octagon
1980°; 152.3°
1080°; 135°
Find the value of each variable.
15.
120°
x°
50°
130°
16.
105°
17.
145°
90°
32°
162°
122°
95°
y°
x 85°
w°
77°
105°
y 155°
w 147°
7-5 Coordinate Geometry
Find the coordinates of the midpoint of each segment.
18.
19.
y
A
4
3
2
1
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
y
Y
x
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
X
1 2 3 4
12 , 12
B
4
3
2
1
x
1 2 3 4
(2, 1)
7-6 Congruence
Z
Write a congruence statement for each pair of polygons.
20.
21.
F
H
121°
36°
121°
D
E
62°
Q
58°
I
23°
120°
P
G
120° W
R
60°
120° X
S
Y
quadrilateral PQRS quadrilateral XYZW
triangle DEF triangle HGI
Copyright © by Holt McDougal.
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162
Holt McDougal Mathematics
CHAPTER 7 REVIEW CONTINUED
7-7 Transformations
22. Graph a reflection across
the x-axis.
y
y
B
4
3
2
1
A
23. Graph a rotation 90° clockwise
about the origin.
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
4
3
2
1
C
x
y
B
4
3
2
1
A
O
A'
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
x
O
ⴚ4ⴚ3 –2 ⴚ1
ⴚ1
ⴚ2
ⴚ3
ⴚ4
1 2 3 4
B
A
2 3 4
D
C
y
4
3
2
1
C
x
A
B
x
O
ⴚ4ⴚ3 –2 ⴚ1
2 3 4
ⴚ1
A'
ⴚ2
ⴚ3
ⴚ4
D B'
C
C'
1 2 3 4
C'
B'
7-8 Symmetry
Complete each figure. The dashed line is the line of symmetry.
24.
25.
26.
Complete each figure. The point is the center of rotation.
27. 4-fold
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All rights reserved.
28. 2-fold
163
Holt McDougal Mathematics
CHAPTER
Big Ideas
7
Answer these questions to summarize the important concepts from
Chapter 7 in your own words.
1. Explain the difference between complementary angles and supplementary
angles.
Complementary angles are angles whose sum measures add to 90°.
Supplementary angles are angles whose sum measures add to 180°.
2. If ⬔1 is 50°, explain how to find m⬔5.
⬔1 ⫽ 50° so ⬔6 ⫽ 50° because
corresponding angles are congruent.
⬔6 and ⬔5 are supplementary angles,
therefore 180° ⫺ m⬔6 ⫽ m⬔5;
180° ⫺ 50° ⫽ 130°. m⬔5 ⫽ 130°.
2 1
3 4
5 6
7 8
3. If the measures of two angles in a triangle are 43° and 74°, explain how to
find the measure of the third angle.
The Triangle Sum Theorem states that the angle measures of a
triangle add to 180°. Two of the three angle measures are known, so
subtract the known angle measures from 180°: 180° ⫺ 43° ⫺ 74° ⫽
63°. The measure of the third angle in the triangle is 63°.
4. Explain how to rotate a figure with vertices A(–1, 5), B(4, 5), C(4, –2), and
D(–1, –2) 90° counterclockwise about the origin. Give the coordinates of
the image.
Multiply each y-coordinate by –1, and then switch the x- and
y-coordinates:
A’ (⫺1, ⫺1 • 5) → A’ (⫺1, ⫺5) → A’ (⫺5, ⫺1); B’ (4, ⫺1 • 5) →
B’ (4, ⫺5) → B’ (⫺5, 4); C’ (4, ⫺1 • ⫺2) → C’ (4, 2) → C’ (2, 4);
D’ (⫺1, ⫺1 • ⫺2) → D’ (⫺1, 2) → D’ (2, ⫺1).
For more review of Chapter 7:
• Complete the Chapter 7 Study Guide and Review on pages 380–382 of
your textbook.
• Complete the Ready to Go On quizzes on pages 358 and 376 of your
textbook.
Copyright © by Holt McDougal.
All rights reserved.
164
Holt McDougal Mathematics