2D Geometry Chapter Questions
1. Name the different types of transformations.
2. Explain how to tell which figure is the pre-image and which is the image.
3. How are dilations different from translations and how are they different from reflections?
4. How are the coordinates of a pre-image affected by a translation? By a rotation?
5. If two parallel lines are cut by a transversal, name the types of angles that are congruent.
6. Explain why a remote exterior angle is equal to the sum the opposite interior angles.
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Chapter Problems
Translations
Class work
Complete the translation and write the rule to describe the translation.
1. Translate the figure right 2 units and up 1
4. Translate the figure right 7 units and down
unit.
3 units.
a. (x, y)
a. (x, y)
5. Translate the figure left 3 units.
a. (x, y)
2. Translate the figure up 1 unit.
a. (x, y)
3. Translate the figure left 1 unit and down 2
units.
a. (x, y)
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6. Translate the figure left 2 units and up 4
units.
a. (x, y)
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Homework
Complete the translation and write the rule to describe the translation.
7. Translate the figure left 3 units and up 3
10. Translate the figure right 1 unit and up 2
units.
units.
a. (x, y)
a. (x, y)
8. Translate the figure right 2 units and up 2
units.
a. (x, y)
11. Translate the figure down 4 units.
a. (x, y)
9. Translate the figure left 3 units and down 4
units.
a. (x, y)
12. Translate the figure right 4 units and down
2 units.
a. (x, y)
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Rotations
Class work
Describe the rotation about the origin pictured from Figure 1 to Figure 2.
13.
Complete the described rotation.
14. A rotation of 90° clockwise about the origin.
15. A rotation of 180° clockwise about the origin.
Describe each rotation about the origin in another way.
16. 40° clockwise
17. 125° counter-clockwise
18. 200° counter-clockwise
19. 250° clockwise
20. 180° clockwise
Name the coordinates of the point after the described rotation about the origin.
21. A (5, -2) 90° clockwise
22. H (-3, -4) 90° counter-clockwise
23. B (12, -8) half-turn
24. X (-8, 2) 90° clockwise
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PARCC-type Questions:
25. Parallelogram A’B’C’D’ (not shown) is the image of parallelogram ABCD after a rotation of 90°
clockwise about the origin. Which statements about parallelogram A’B’C’D’ are true? Select each
correct statement.
a) ̅̅̅̅̅̅
𝐴′𝐵′ is perpendicular to ̅̅̅̅
𝐵𝐶
̅̅̅̅̅̅
̅̅̅̅̅̅
b) 𝐴′𝐵′ is parallel to 𝐶′𝐷′
̅̅̅̅̅̅
c) ̅̅̅̅̅̅
𝐴′𝐵′ is parallel to 𝐴′𝐷′
̅̅̅̅̅̅ is perpendicular to ̅̅̅̅
d) 𝐴′𝐵′
𝐴𝐵
̅̅̅̅̅̅ is parallel to ̅̅̅̅̅̅
e) 𝐴′𝐷′
𝐵′𝐶′
̅̅̅̅̅̅ is parallel to ̅̅̅̅̅̅
𝐴′𝐷′
𝐶′𝐷′
f)
26. Rhombus E’F’G’H’ (not shown) is the image of rhombus EFGH after a rotation of 90° clockwise about
the origin. Which statements about rhombus E’F’G’H’ are true? Select each correct statement.
a) ̅̅̅̅̅
𝐸′𝐹′ is parallel to
b) ̅̅̅̅̅
𝐸′𝐹′ is parallel to
̅̅̅̅̅
𝐹′𝐺′
̅̅̅̅̅̅
𝐺′𝐻′
c) ̅̅̅̅̅
𝐸′𝐹′ is parallel to ̅̅̅̅̅̅
𝐸′𝐻′
̅̅̅̅̅ is parallel to ̅̅̅̅̅̅
d) 𝐹′𝐺′
𝐺′𝐻′
e) ̅̅̅̅̅
𝐹′𝐺′ is parallel to ̅̅̅̅̅̅
𝐸′𝐻′
f)
̅̅̅̅̅̅
𝐺′𝐻′ is parallel to ̅̅̅̅̅̅
𝐸′𝐻′
Homework
27. Describe the rotation about the origin pictured from Figure 1 to Figure 2.
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Complete the described rotation.
28. A rotation of 90° clockwise about the origin.
29. A rotation of 180° clockwise about the origin.
Describe each rotation about the origin in another way.
30. 15° counter-clockwise
31. 210° clockwise
32. 130° counter-clockwise
33. 300° clockwise
34. 175° clockwise
Name the coordinates of the point after the described rotation about the rotation.
35. F (-4, -9) 90° counter-clockwise
36. G (8, -2) 90° clockwise
37. R (-5, 2) 90° counter-clockwise
38. T (4, -13) Half-turn
PARCC-type Questions:
39. Trapezoid A’B’C’D’ (not shown) is the image of trapezoid ABCD after a rotation of 90°
counterclockwise about the origin. Which statements about trapezoid A’B’C’D’ are true? Select
each correct statement.
̅̅̅̅̅̅
a) ̅̅̅̅̅̅
𝐵′𝐶′ is parallel to 𝐴′𝐷′
b) ̅̅̅̅̅̅
𝐴′𝐵′ is parallel to ̅̅̅̅̅̅
𝐶′𝐷′
̅̅̅̅̅̅ is congruent to ̅̅̅̅̅̅
c) 𝐴′𝐷′
𝐵′𝐶′
̅̅̅̅̅̅ is congruent to 𝐶′𝐷′
̅̅̅̅̅̅
d) 𝐴′𝐷′
e) ̅̅̅̅̅̅
𝐶′𝐷′ is perpendicular to ̅̅̅̅
𝐶𝐷
̅̅̅̅̅̅
f) 𝐶′𝐷′ is perpendicular to ̅̅̅̅
𝐵𝐶
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40. Rectangle E’F’G’H’ (not shown) is the image of rectangle EFGH after a rotation of 90° clockwise
about the origin. Which statements about rectangle E’F’G’H’ are true? Select each correct
statement.
a) ̅̅̅̅̅
𝐸′𝐹′ is parallel to ̅̅̅̅̅̅
𝐺′𝐻′
̅̅̅̅̅
b) 𝐸′𝐹′ is parallel to ̅̅̅̅̅̅
𝐸′𝐻′
c) ̅̅̅̅̅
𝐹′𝐺′ is perpendicular to ̅̅̅̅̅̅
𝐸′𝐻′
̅̅̅̅̅
d) 𝐹′𝐺′ is perpendicular to ̅̅̅̅̅̅
𝐺′𝐻′
̅̅̅̅̅̅ is perpendicular to 𝐸′𝐹′
̅̅̅̅̅
e) 𝐺′𝐻′
f) ̅̅̅̅̅̅
𝐺′𝐻′ is perpendicular to ̅̅̅̅̅̅
𝐸′𝐻′
Reflections Class work
41. Give an example in nature of a reflection.
Complete the described reflections.
42.
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44.
47.
45.
Homework
Complete the described reflections.
48.
49.
Describe the reflection shown in each graph.
46.
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Describe the reflection shown in each graph.
52.
50.
53.
51.
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PARCC-type Questions
54. Three congruent figures are shown on the coordinate plane. Use the figures to answer the next two
questions. Select a transformation from each group of choices to make the statement true.
Part A:
Figure 1 can be transformed to figure 2 by:
a) a reflection across the y-axis
b) a rotation of 90° counterclockwise
about the origin
c) a translation 4 units left
followed by
d) a translation 6 units down
e) a reflection across the x-axis
f) a rotation of 180° about the origin
Part B:
Transforming figure 1 with a sequence of 2 transformations can also create figure 3. Figure 1 can be
transformed to figure 3 by:
a) a rotation of 90 clockwise about the origin
b) a translation 8 units down
c) a reflection across the x-axis
followed by
d) a rotation 90 counterclockwise about the origin
e) a translation 4 units right and 3 units down
f) a reflection across the y-axis
Dilations
Class work
55. Given a scale factor of 3, what happens to the coordinates for the dilation of a pre-image?
Given the coordinates of the pre-image and the scale factor, find the coordinates of the image.
56. R (-3, 6); scale factor = ½
57. W (2, 9); scale factor = 3
58. D (4, -2); scale factor = 4
59. Q (1, -3); scale factor = 1.5
Given the coordinates of the pre-image and image, determine the scale factor.
60. (4, -2)
(8, -4)
61. (-3, -1)
(-9, -3)
62. (0, -5)
(0, -2.5)
63. (8, 12)
(2, 3)
64. (5, -4)
(12.5, -10)
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Homework
65. Given a scale factor of ½, what happens to the coordinates for the dilation of a pre-image?
Given the coordinates of the pre-image and the scale factor, find the coordinates of the image.
66. G (2, 4); scale factor = 2
67. J (-3, 9); scale factor = ⅓
68. T (-4, 5); scale factor = 3½
69. Y (-2, 6); scale factor = 4
Given the coordinates of the pre-image and image, determine the scale factor.
70. (3, -5)
(9, -15)
71. (-2, 7)
(-4, 14)
72. (8, 0)
(2, 0)
73. (3, -8)
(4.5, -12)
74. (6, 3)
(3, 1.5)
Symmetry
Class work
Draw all lines of symmetry for the figure shown.
75.
76.
Determine if the figure has rotational symmetry. If so, list the degrees where it occurs.
77.
78.
79.
80.
Homework
Draw all lines of symmetry for the figure shown.
81.
82.
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Determine if the figure has rotational symmetry. If so, list the degrees where it occurs.
83.
84.
85.
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Congruence & Similarity
Class work
For each problem:
 Determine if the two figures are congruent, similar, or neither.
 Explain how one figure was obtained from the other through a series of translations, rotations,
reflections and/or dilations.
87.
90.
88.
91.
89.
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Homework
For each problem:
 Determine if the two figures are congruent, similar, or neither.
 Explain how one figure was obtained from the other through a series of translations, rotations,
reflections and/or dilations
92.
95.
93.
96.
94.
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Special Pairs of Angles
Class work
Using the figure shown, name as many of the following
pairs of angles as you can find.
97. Vertical Angles
98.
Alternate Interior Angles
99.
Alternate Exterior Angles
100.
Same Side Interior Angles
101.
Adjacent Angles
102.
Corresponding Angles
Using what you know about special pairs of angles, find the missing measure(s) in each figure.
103.
104.
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105.
Homework
Using the figure shown, name as many of the following pairs of angles as you can find.
106. Vertical Angles
107.
Alternate Interior Angles
108.
Alternate Exterior Angles
109.
Same Side Interior Angles
110.
Adjacent Angles
111.
Corresponding Angles
Using what you know about special pairs of angles, find the missing measure(s) in each figure.
112.
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113.
114.
Remote Exterior Angles
Class work
Based on the Remote Exterior Angle Theorem, find the missing angle. (diagrams NOT drawn to scale)
115.
116.
30°
70°
50°
x°
x°
117.
118.
x°
x°
130°
165°
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Based on the Remote Exterior Angle Theorem, find the value of x. (diagrams NOT drawn to scale)
119.
100°
20°
(2x)°
120.
(2x – 20)°
(x + 5)°
(x – 15)°
121.
(5x – 31)°
(3x – 1)°
(4x)°
122.
25°
°
(4x)°
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Remote Exterior Angles
Homework
Based on the Remote Exterior Angle Theorem, find the missing angle. (diagrams NOT drawn to scale)
123.
124.
95°
x°
75°
x°
35°
125.
126.
x°
(2x)°
120°
150°
Based on the Remote Exterior Angle Theorem, find the value of x. (diagrams NOT drawn to scale)
127.
80°
70°
(3x)°
128.
(x – 7)°
21°
(3x)°
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129.
x°
(5x – 6)°
(2x + 86)°
(7x + 4)°
130.
(x – 9)°
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Unit Review
2D Geometry Multiple Choice Questions
1. What rule describes the translation left 3 units and up 4 units?
a. (x,y) →(x + 3, y + 4)
b. (x,y) →(x + 3, y - 4)
c. (y, x) →(x – 3, y + 4)
d. (x,y) →(x – 3, y + 4)
2. What translation does the rule (x,y) →(x – 7, y) describe?
a. Right 7 units
b. Left 7 units
c. Up 7 units
d. Down 7 units
3. What direction are rotations unless you are told otherwise?
a. clockwise
b. south
c. counterclockwise
d. north
4. What are the new coordinates of a point A (3, -2) after a 90° rotation
counterclockwise about the origin?
a. (3, 2)
b. (-3, 2)
c. (-3, -2)
d. (2, 3)
5. What are the new coordinates of a point B (-5, 8) after a half-turn rotation about the
origin?
a. (-8, -5)
b. (-5, -8)
c. (8, 5)
d. (5, -8)
6. What are the coordinates of a point C (-1, 6 ) after a dilation with respect to the origin
with a scale factor of 1/3?
a. (-3, 18)
b. (6, -1)
c. (-1/3, 2)
d. (3, -18)
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7. What is the scale factor of a point if it changes as follows after a dilation with respect
to the origin?
(4, 23)
(20, 115)
a. -5
b. 5
c. 16
d. 1/5
8. How many lines of symmetry does the figure have?
a. 10
b. 3
c. 5
d. 0
9. Determine if the figure has rotational symmetry. If so, list the degrees where it occurs.
a. Rotational Symmetry; 180°
b. Rotational Symmetry; 90°, 180°, 360°
c. Rotational Symmetry; 90°, 180°, 270°, 360°
d. No Rotational Symmetry
10. What makes two figures similar?
a. same size, same shape
b. same shape, different angles, proportional sides
c. same shape, congruent angles, proportional sides
d. same size, same shape, different angles
11. Which of the following terms best describes the two figures?
a. congruent
b. similar
c. neither congruent nor similar
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12. Trapezoid B’C’D’E’ (not shown) is the image of trapezoid BCDE after a rotation of
180° about the origin. Which statements about trapezoid B’C’D’E’ are true. Select
each correct statement.
g) ̅̅̅̅̅̅
𝐵′𝐶′ is parallel to
h) ̅̅̅̅̅̅
𝐵′𝐶′ is parallel to
̅̅̅̅
𝐵𝐶
̅̅̅̅̅̅
𝐶′𝐷′
̅̅̅̅̅̅ is parallel to ̅̅̅̅
𝐵′𝐸′
𝐶𝐷
j) ̅̅̅̅̅̅
𝐵′𝐸′ is parallel to ̅̅̅̅̅̅
𝐶′𝐷′
̅̅̅̅̅̅
k) 𝐵′𝐸′ is parallel to ̅̅̅̅̅̅
𝐵′𝐶′
̅̅̅̅̅̅
l) 𝐵′𝐸′ is parallel to ̅̅̅̅̅̅
𝐷′𝐸′
i)
For 13 - 16, use the figure shown.
13. What are the vertical angles?
a. ∠ 1 & ∠ 2 ; ∠ 3 & ∠ 4
b. ∠ 5 & ∠ 6 ; ∠ 7 & ∠ 8
c. ∠ 1 & ∠ 4 ; ∠ 5 & ∠ 8 ; ∠ 2 & ∠ 4 ; ∠ 6 & ∠ 8
d. ∠ 1 & ∠ 4 ; ∠ 2 & ∠ 3 ; ∠ 5 & ∠ 8 ; ∠ 6 & ∠ 7
Figure: Note: ℓ || 𝑚
14. What are the alternate interior angles?
a. ∠ 3 & ∠ 6 ; ∠ 4 & ∠ 5
b. ∠ 1 & ∠ 8 ; ∠ 2 & ∠ 7
c. ∠ 1 & ∠ 2 ; ∠ 5 & ∠ 6
d. ∠ 3 & ∠ 4 ; ∠ 7 & ∠ 8
15. What is the relationship between ∠ 2 and ∠ 7?
a. alternate exterior angles
b. alternate interior angles
c. complimentary angles
d. vertical angles
16. What is the relationship between ∠ 4 and ∠ 6?
a. supplementary angles
b. complementary angles
c. alternate interior angles
d. vertical angles
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Use the diagram to the right to answer questions 17-19.
Diagram NOT drawn to scale.
17. If m∠1 = 67° and m∠2 = 38°, then what is the
measure of ∠4?
a. not enough information
b. 100°
c. 75°
d. 105°
2
1
3
4
18. If m∠1 = 72° and m∠4 = 108°, then what is the
measure of ∠2?
a. not enough information
b. 36°
c. 72°
d. 85°
19. If m∠1 = (3x)°, and the m∠2 = (5x)°, and m∠4 = (180 – x)° then what is x?
a. 30°
b. 20°
c. 40°
d. not enough information
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2D Geometry Short Constructed Response Questions
20. Translate the figure shown using the following rule: (x,y)
21.
(x – 11, y + 4)
Rotate the figure 270º clockwise about the origin.
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22. Reflect the figure across the x-axis.
23. Describe the following rotations in another way:
a. 63° clockwise about the origin
b. 237° counterclockwise about the origin
c. 55° counterclockwise about the origin
24. Circle the following figures that have symmetry:
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25. List three different pairs of angles that are supplementary.
26. List three different pairs of angles that are complementary.
2D Geometry Extended Constructed Response Questions
27.
Draw a figure on graph paper. Label the coordinates. Write the following
rules in your own words. Apply the following rules to your object. Label the
coordinates of your transformed object.
(x + 4, y – 3)
a. translate: (x,y)
b. rotate 90° counterclockwise about the origin
c. reflect across the x axis.
28.
Draw a figure on graph paper with at least three lines of symmetry. Label
the lines of symmetry.
29.
Given that ℓ || 𝑚 & 𝑚∠2 = 110°, fill in all the angle measurements in the
following figure:
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Answer Key
1. (x, y)
(x+2, y+1)
2. (x, y)
(x, y+1)
3. (x, y)
4. (x, y)
(x+7, y-3)
5. (x, y)
(x-3, y)
6. (x, y)
(x-2, y+4)
(x-1, y-2)
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7. (x, y)
(x-3, y+3)
8. (x, y)
(x+2, y+2)
9. (x, y)
(x-3, y-4)
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10. (x, y)
(x+1, y+2)
11. (x, y)
(x, y-4)
12. (x, y)
(x+4, y-2)
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13. 180° / Half-turn
14.
29. A rotation of 180° clockwise about the
origin
15. A rotation of 180° clockwise about the
origin
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
320° CCW
235° CW
160° CW
110° CCW
180° CCW / Half-turn
A’ (-2, -5)
H’ (4, -3)
B’ (-12, 8)
X’ (2, 8)
b, d, e
b, e
180° CCW / Half-turn
A rotation of 90° clockwise about the
origin
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30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
345° CW
150° CCW
230° CW
60° CCW
185° CCW
F’ (9, -4)
G’ (-2, -8)
R’ (-2, -5)
T’ (-4, 13)
b, c, e
a, d, f
Answers will vary.
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44.
49.
45.
50.
46. Across y= -1
47. Across y = x
51.
48.
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52. Across x= 2
53. Across x-axis
54. Part A: b & d
Part B: c & e
55. They are multiplied by 3
56. R’ (-1½, 3)
57. W’ (6, 27)
58. D’ (16, -8)
59. Q’ (1½, -4.5)
60. SF = 2
61. SF = 3
62. SF = ½
63. SF =
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
81.
82.
1
4
SF = 2½
They are multiplied by ½
G’ (4, 8)
J’ (-1, 3)
T’ (-14, 17.5)
Y’ (-8, 24)
SF = 3
SF = 2
SF = ¼
SF = 1½
SF = ½
83.
84.
85.
86.
87. Similar; Dilation
Yes; 120°, 240°
Yes; 60°, 120°, 180°, 240°, 300°
Yes; 180°
No
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2
; (x, y)
3
(x+5, y-2)
88. Congruent; Reflect over y-axis;
(x, y)
(x, y-3)
89. Congruent: (x, y)
(x-8, y-5)
90. Congruent; Rotate 90° CCW
91. Similar; Dilation Scale Factor ¼; Rotate
90° CCW
92. Congruent; Reflect over y=3;
(x, y)
(x+3, y)
93. Congruent; Rotate 90° CW, translate
right 2 units, translate down 2 units
94. Similar; Dilation Scale Factor ½; Reflect
over y-axis
95. Similar; Dilation S.F. 2;
(x, y) (x-12, y-8)
96. Congruent; Rotate 90° CW, than
Reflection over y=0 OR
Reflection over line y = -x
97. ∠1, ∠4 ∠2, ∠3 ∠5, ∠8 ∠6, ∠7
98. ∠3, ∠6 ∠4, ∠5
99. ∠1, ∠8 ∠2, ∠7
100.
∠3, ∠5 ∠4, ∠6
101.
∠1, ∠3 ∠2, ∠4 ∠5, ∠7
∠6, ∠8 ∠1, ∠2 ∠3, ∠4 ∠5, ∠6
∠7, ∠8
76.
77.
78.
79.
80.
Yes; 72°, 144°, 216°, 288°
Yes; 180°
Yes; Infinitely Many
None
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102.
∠1, ∠5 ∠2, ∠6 ∠3, ∠7
∠4, ∠8
103.
∠1 = ∠4 = ∠5 = 70°
∠2 = ∠3 = ∠6 = ∠7 = 110°
104.
∠2 = 115° ∠1 = ∠4 = 65°
105.
∠7 = 105° ∠5 = ∠8 = 75°
106.
∠8, ∠4 ∠6, ∠3 ∠1, ∠2 ∠5, ∠7
107.
∠5, ∠6 ∠1, ∠8
108.
∠4, ∠2 ∠3, ∠7
109.
∠1, ∠6 ∠8, ∠5
∠3, ∠4 ∠6, ∠4 ∠6, ∠8 ∠8, ∠3
∠1, ∠5 ∠5, ∠2 ∠7, ∠2 ∠1, ∠7
111.
∠1, ∠4 ∠5, ∠3 ∠6, ∠7 ∠8, ∠2
112.
∠8 = ∠4 = ∠5 = 45°
∠2 = ∠3 = ∠6 = ∠7 = 135°
113.
∠1 = ∠4 = 67°
∠3 = 113°
∠5 = ∠8, unknown because lines are
not parallel
∠6 = ∠7, unknown because lines are
not parallel
114.
∠1 = ∠5 = ∠8 = 55°
∠2 = ∠3 = ∠6 = ∠7 = 125°
115.
80°
116.
140°
117.
80°
118.
75°
119.
60°
120.
x = 20
121.
x=5
122.
x = 35
123.
130°
124.
140°
125.
x = 30
126.
x = 60°
127.
x = 50
128.
x=7
129.
x = 46
130.
x=6
110.
6. c
7. b
8. c
9. c
10. c
11. b
12. a, c & d
13. d
14. a
15. a
16. a
17. d
18. b
19. b
20. A’(-3,-1); B’(-6,-1); C’( -7,1)
21. A’(3,-2); B’(6,2); C’(6,7); D’(3,7)
22. A’(-3,-2); B’(-6,-2); C’(-6,-7); D’(-3,7)
23.
a. 297° counterclockwise
b. 123° clockwise
b. 305° clockwise
24. square, flower, and arrow should be
circled.
25. answers will vary
26. answers will vary
27. answers will vary
28. answers will vary
29. ∠1,∠4,∠5,∠8 = 70°
∠3,∠6,∠7 = 110°
Unit Review Answers
1. d
2. b
3. c
4. d
5. d
NJ Center for Teaching and Learning
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