Download 2d-geometry-classwork-homework-2012-08

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 reflections?
4. How are the coordinates of a pre-image affected by a translation? Rotation?
5. If two parallel lines are cut by a transversal, name the types of angles that are congruent.
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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
unit.
a. (x, y)
2. Translate the figure up 1 unit.
a. (x, y)
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3. Translate the figure left 1 unit and down 2
units.
a. (x, y)
4. Translate the figure right 7 units and down
3 units.
a. (x, y)
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5. Translate the figure left 3 units.
a. (x, y)
Homework
Complete the translation and write the rule to
describe the translation.
7. Translate the figure left 3 units and up 3
units.
a. (x, y)
6. Translate the figure left 2 units and up 4
units.
a. (x, y)
8. Translate the figure right 2 units and up 2
units.
a. (x, y)
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9. Translate the figure left 3 units and down 4
units.
a. (x, y)
10. Translate the figure right 1 unit and up 2
units.
a. (x, y)
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11. Translate the figure 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
13. Describe the rotation pictured from Figure 1 to Figure 2.
Complete the described rotation.
14.
15.
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Describe each rotation 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.
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
Homework
25. Describe the rotation pictured from Figure 1 to Figure 2.
Complete the described rotation.
26.
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27.
Describe each rotation in another way
28. 15° counter-clockwise
29. 210° clockwise
30. 130° counter-clockwise
31. 300° clockwise
32. 175° clockwise
Name the coordinates of the point after the described rotation.
33. F (-4, -9) 90° counter-clockwise
34. G (8, -2) 90° clockwise
35. R (-5, 2) 90° counter-clockwise
36. T (4, -13) Half-turn
Reflections Class work
37. Give a example in nature of a reflection.
Complete the described reflections.
38.
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39.
y = -1
Describe the reflection shown in each graph.
42.
40.
43.
41.
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Homework
Complete the described reflections.
44.
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45.
Describe the reflection shown in each graph.
48.
46.
49.
47.
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Dilations
Class work
50. What happens to the coordinates in a dilation with a scale factor of 3?
Given the coordinates of the pre-image and the scale factor, find the coordinates of the image.
51. R (-3, 6); scale factor = ½
52. W (2, 9); scale factor = 3
53. D (4, -2); scale factor = 4
54. Q (1, -3); scale factor = 1.5
Given the coordinates of the pre-image and image, determine the scale factor
55. (4, -2)
(8, -4)
56. (-3, -1)
(-9, -3)
57. (0, -5)
(0, -2.5)
58. (8, 12)
(2, 3)
59. (5, -4)
(12.5, 10)
Homework
60. What happens to the coordinates in a dilation with a scale factor of ½ ?
Given the coordinates of the pre-image and the scale factor, find the coordinates of the image.
61. G (2, 4); scale factor = 2
62. J (-3, 9); scale factor = ⅓
63. T (-4, 5); scale factor = 3½
64. Y (-2, 6); scale factor = 4
Given the coordinates of the pre-image and image, determine the scale factor
65. (3, -5)
(9, -15)
66. (-2, 7)
(-4, 14)
67. (8, 0)
(2, 0)
68. (3, -8)
(4.5, -12)
69. (6, 3)
(3, 1.5)
Symmetry
Class work
Draw all lines of symmetry for the figure shown.
70.
71.
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Determine if the figure has rotational symmetry. If so, list the degrees where it occurs.
72.
73.
74.
75.
Homework
Draw all lines of symmetry for the figure shown.
76.
77.
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Determine if the figure has rotational symmetry. If so, list the degrees where it occurs.
78.
79.
80.
81.
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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.
82.
83.
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84.
85.
86.
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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.
87.
88.
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89.
90.
91.
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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.
92. Vertical Angles
93. Alternate Interior Angles
94. Alternate Exterior Angles
95. Same Side Interior Angles
96. Adjacent Angles
97. Corresponding Angles
Using what you know about special pairs of angles, find the missing measure(s) in each figure.
98.
99.
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100.
Homework
Using the figure shown, name as many of the following pairs of angles as you can find.
101.
102.
103.
104.
105.
106.
Vertical Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior Angles
Adjacent Angles
Corresponding Angles
Using what you know about special pairs of angles, find the missing measure(s) in each figure.
107.
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108.
109.
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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?
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?
a. (-8, -5)
b. (-5, -8)
c. (8, 5)
d. (5, -8)
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6. What are the coordinates of a point C( -1, 6 ) after a dilation with a scale factor of
1/3?
a. (-3, 18)
b. (6, -1)
c. (-1/3, 2)
d. (3, -18)
7. What is the scale factor of a point if it changes as follows after a dilation?
( 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 size, different angles
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11. Which of the following terms best describes the two figures?
a. congruent
b. similar
c. neither congruent nor similar
For 12 - 15, use the figure shown.
12. 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:
13. 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
14. What is the relationship between ∠ 2 and ∠ 7?
a. alternating exterior angles
b. alternating interior angles
c. complimentary angles
d. vertical angles
15. What is the relationship between ∠ 4 and ∠ 6?
a. supplementary angles
b. complementary angles
c. alternating interior angles
d. vertical angles
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2D Geometry Short Constructed Response Questions
16. Translate the figure shown using the following rule: (x,y)
( x + 4, y - 11)
17. Rotate the figure 270º clockwise about the origin.
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18. Reflect the figure across the x-axis.
19. Describe the following rotations in another way:
a. 63° clockwise
b. 237° counterclockwise
c. 55° counterclockwise
20. Circle the following figures that have symmetry:
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21. List three different pairs of angles that are supplementary.
22. List three different pairs of angles that are complementary.
2D Geometry Extended Constructed Response Questions
23. 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.
a. translate: (x,y)
(x+4, y - 3)
b. rotate 90 counterclockwise
c. reflect across the x axis.
24. Draw a figure on graph paper with at least three lines of symmetry. Label the lines of
symmetry.
25. Fill in all the angle measurements in the following figure:
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