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2D Geometry: Chapter Questions
1. What are some of the special relationships between angles?
2. What are perimeter and circumference and how are they relevant in daily life?
3. How is the formula for area of a parallelogram related to area of a rectangle?
4. How is the formula for area of a triangle related to area of a rectangle?
5. How do you find the area of irregular shapes?
6. How do you find the area of shaded regions?
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2D Geometry: Chapter Problems
Special Pairs of AnglesClasswork1. If two angles have the same measure are they congruent?2. Angle 1 and Angle 2 are complementary. If ∠1 has a measure of 42o what would the measure of
∠2 be?3. Determine the measure of ∠3 in the figure below.
4. What is the complement of 72o?5. If Angle 1 measures 48o and Angle 2 measures 42o are these angles complementary?6. Angle R and S are supplementary. If Angle R measures 115o what is the measure of Angle S?7. What is the measure of angle 4?
8. What is the supplement of 72o?9. If Angle X measures 53o and Angle Y measures 127o are these angles supplementary?10. What is the complement of 68o? Supplement?11. Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
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Angle Measurement Reason
∠1 65° Given
∠2
∠3
∠4
12. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 37o determine the measures of the remaining angles. You must be able to explain why.
Homework13. Angle M has a measure of 36o and Angle N has a measure of 24o. Are these two angles congruent?14. Angle R and Angle S are complementary. If ∠ S has a measure of 26o what would be the measure of
∠R?15. Determine the measure of the unknown angle 5 in the figure below.
16. What is the complement of 9o?17. If Angle X measures 53o and Angle Y measures 127o are these angles complimentary?18. Angle A and B are supplementary. If ∠ A measures 97o what is the measure of ∠B?19. What ism∠ 6?
20. What is the supplement of 9o?21. If m∠1=¿ 48o and m∠2=¿ 42o are these angles supplementary?
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Angle Measurement Reason
∠1
∠2
∠3
∠4
∠6
∠7
∠8
22. What is the complement of 84o? Supplement?23. Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
24. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 68o determine the measures of the remaining angles. You must be able to explain why.
Perimeter and CircumferenceClassworkFind the perimeter of each figure.25.
26.
27.
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28.
In #29-33, use 3.14 as your value of π.29. Determine the circumference of a circle with radius 5 cm.
30. Determine the circumference of a circle with radius 2.3 m.
31. Determine the circumference of a circle whose diameter is 8 m.
32. Determine the circumference of a circle whose diameter is 24.6 cm.
33. What is the diameter of a circle whose circumference is 47.1 m?
In #34-38, leave your answer in terms of π.34. Determine the circumference of a circle with radius of 4 m.
35. Determine the circumference of a circle with radius of 3.6 cm.
36. Determine the circumference of a circle whose diameter is 10 m.
37. Determine the circumference of a circle whose diameter is 31.5 cm.
38. What is the radius of a circle whose circumference is 10.5π in?
HomeworkFind the perimeter of each figure.39.
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40.
41.
42.
In #43-47, use 3.14 as your value of π.43. Determine the circumference of a circle whose radius is 3.5 m.
44. Determine the circumference of a circle whose radius is 32 inches.
45. Determine the circumference of a circle whose diameter is 32 inches.
46. Determine the circumference of a circle with diameter 8 feet.
47. What is the radius of a circle whose circumference is 13.188 cm?
In #48-52, leave your answer in terms of π.48. Determine the circumference of a circle with radius of 5.5 m.
49. Determine the circumference of a circle with radius of 24 in.
50. Determine the circumference of a circle whose diameter is 24 m.
51. Determine the circumference of a circle whose diameter is 12 feet.
52. What is the radius of a circle whose circumference is 11.4 π in?
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Rectangles & ParallelogramsClassworkFind the area of each figure.
53.
54.
55.
56.
57.
58. The length of a rectangle is 10 in and the width is 3 in. What is its area?
59. How do you find the area of a rectangle?
60. How do you find the area of a parallelogram?
61. What is true of the base and height of a parallelogram?
62. What is the base of a parallelogram whose height is 4 cm and whose area is 44 cm2?
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HomeworkFind the area of each figure.
63.
64.
65.
66.
67.
68. The length of a rectangle is 17 m and the width is 6 m. What is its area?
69. How do you find the area of a rectangle?
70. How do you find the area of a parallelogram?
71. What is true of the base and height of a parallelogram?
72. What is the base of a parallelogram whose height is 7 cm and whose area is 63 cm2?
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Triangles & TrapezoidsClassworkFind the area of each figure.
73.
74.
75.
76.
77.
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78. Find the height of a triangle whose area is 20 in2 and whose base is 8 in.
Homework
Find the area of each figure.
79.
80.
81.
82.
83.
84. Find the height of a triangle whose area is 25 in2 and whose base is 5 in.
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Circles
Classwork
Find the area of each figure. Use 3.14 as your value of π .
85.
86.
In #87-90, use 3.14 as your value of π.87. A goat is tied to a 5 m rope. What is the area of the grass he can eat?88. What is the area of a circle with a radius of 7 cm?89. What is the area of a circle with a diameter of 16 yd?90. How do you find area of a circle when given radius?
Find the area of each figure. Leave your answer in terms of π.91.
92.
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In #93-95, leave your answer in terms of π.93. A goat is tied to an 8 m rope. What is the area of the grass he can eat?94. What is the area of a circle with a radius of 10 cm?95. What is the area of a circle with a diameter of 22 yd?
Homework
Find the area of each figure. Use 3.14 as your value of π .96.
97.
In #98-101, use 3.14 as your value of π.98. A circular sprinkler has a radius of 4 m. How much grass can the sprinkler water?99. What is the area of a circle with a radius of 5 in?100. What is the area of a circle with a diameter of 14 m?101. How do you find area of a circle when given diameter?
Find the area of each figure. Leave your answer in terms of π.102.
103.
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In #104-106, leave your answer in terms of π.104. A circular sprinkler has a radius of 8 m. How much grass can the sprinkler water?105. What is the area of a circle with a radius of 13 in?106. What is the area of a circle with a diameter of 18 m?
Irregular Figures
Classwork
Find the area of each figure.
107.
108.
109.
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110.
Homework
Find the area of each figure.
111.
112.
113. Use 3.14 as your value of π.
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114.
Shaded Figures
Classwork
Find the area of each shaded region. If needed, use 3.14 as your value of π.
115.
116.
117.
Homework
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Find the area of each shaded region. If needed, use 3.14 as your value of π.
118.
119.
120.
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2 Dimensional Geometry – Chapter Review
1. Match each vocabulary word with its definition given to the right.
_____ Vertical Angles a) Two angles that are next to each other and have a common ray
_____ Alternate Interior Angles b) When two lines are crossed by a transversal, the pairs of angles on opposite sides of the transversal and outside of
the two lines._____ Alternate Exterior Angles c) When two lines are crossed by a transversal, the pairs of
angles on opposite sides of the transversal and inside of the two lines.
_____ Adjacent Angles d) When two lines are crossed by a transversal, the pairs of angles that are on the same side of the transversal and in
the same location at each intersection._____ Corresponding Angles e) When two lines are crossed by a transversal, the pairs of
angles on the same side of the transversal and inside of the two lines.
_____ Same-side Interior Angles f) Two angles that are opposite each other when two linesintersect.
2. ABC measures 62. Its complementary angle measures:a. 28b. 62c. 208d. 298
3. In the figure below, j || k and m∠3=82 °. Find the measurements of each remaining angle.
4. What is the perimeter of an equilateral triangle with 6-inch sides?a. 18 inchesb. 24 inchesc. 27 inchesd. 36 inches
5. A soccer field has a length of 100 yards and a width of 60 yards. What is the perimeter of the field?a. 160 yardsb. 220 yardsc. 320 yardsd. 6000 square yards
6. What is the area of a rectangle with length 36 cm and width 4 cm?a. 72 cmb. 144 cmc. 144 cm2
d. 72 cm2
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7. In which picture(s) below are ∠1∧∠2 considered to be congruent angles? Circle all that apply.
a.
b.
c.
d.
e.
f.
8. What is the area of the figure pictured to the right?
9. A triangle has an area of 36 yd2 and a base of 3 yd, what is the height of the triangle?
10. Find the area of the figure to the right.
11. Find the height of the parallelogram with a length of 50 in and an area of 275 in2.
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12. Jewell wants to tile her kitchen floor with tiles that are 1.5 ft2. If her kitchen is 18 ft by 12 ft, how many tiles will she need?
13. Find the area of the figure to the right.
14. Find the area of the shaded region to the right.
15. Find the length of the base of a triangle with an area of 20 cm2 and a height of 5 cm.
16. A circular carpet covers an area of 201 cm2. What is the radius of the carpet? Use 3.14 as your value of π.
17. What is the diameter of a circle whose area is 38.04 in2?
18. In order to decorate for a party, you need to cover 3 rectangular tables with tablecloth. The tables measure 36 in by 72 in. If you want 2 inches overhang on each side, how many square inches of fabric would it take to cover the 3 tables?
19. The doors in your home need to be painted. Each door measures 8 ft x 3 ft. You are amazed that you have 22 doors to paint! A can of paint can cover 400 square feet. How many cans of paint will you need to purchase?
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20. The diagram below shows one side of Joe’s shed. In order for him to install siding on to both sides of his shed, he needed to calculate its total area. Below is a series of steps that Joe took to complete his calculation. Is he correct? If so, explain how all of his steps are correct. If not, explain what he should have done calculate the area correctly.
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Joe’s calculations:Total Area=top area+bottomarea
Total Area=12(12) (4 )+12 (8 )
Total Area=24+96Total Area=120 ft2
Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.
21. Your parents have offered to pay you to wallpaper the kitchen walls. The wallpaper that you want costs $12 per square foot. The rectangular kitchen measures 16 ft x 12 ft, with a height of 8 ft. One doorway measures 8 ft x 3 ft and two windows measures 3 ft x 5 ft.
a. Calculate the area of the kitchen walls, pretending there are no windows or doorways .b. What is the area of the kitchen walls, when the doorways and windows are taken into
account?c. What will be the minimum cost to wallpaper the kitchen?
22. You have been asked to design a flower garden with an area of 52 ft2. The client has no preference for the shape of the garden. It’s all up to you!
a. If it will cost $3/ft to put flowers in the garden, determine the total cost.b. Provide two possible dimensions of the flower garden.c. Identify the shape that has the smallest perimeter.
23. A decorator wants to install two picture windows, measuring 12 ft. x 8 ft. The windows will be placed on a wall measuring 72 ft x 12 ft.
a. What is the area of the wall, without windows?b. How much area will two windows cover?c. Wallpaper, costing $6/square foot, will be purchased to cover the wall, once the windows
are installed. What will be the least amount of money spent on the wallpaper?
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24. A bag of grass seed can cover 120 square feet. Ms. Peabody wants to seed her front and back yard. The front yard is rectangular in shape, measuring 10 ft x 8 ft. Her back yard has an irregular shape and is pictured below.
A. Calculate the square footage of Ms. Peabody’s front yard.B. Calculate the square footage of Ms. Peabody’s back yard.C. How many bags of grass seed will Ms. Peabody need to purchase?
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4
Answer Key
1. Yes2. 48°3. 27°4. 18°5. Yes6. 65°7. 128°8. 108°9. Yes10. Complement = 22°, Supplement = 112°11. Multiple answers for the reasons. Some
examples:∠2 = 65° since it's vertical to a 65° angle and vertical angles are congruent∠3 = 115° since it's supplemental to ∠2 and to the 65° angle∠4 = 115° since it's vertical to ∠3 or supplemental to ∠2
12. Multiple answers for the reasons. Some examples:∠1 = 37° since it's an alternate exterior angle to ∠5 and alternate exterior angles are congruent∠2 = 143° since it's supplemental to ∠1∠3 = 37° since it's vertical to ∠5∠4 = 143° since it's supplemental to ∠3 and ∠5 or since it corresponds to ∠2∠6 = 143° since it's vertical to ∠4 or since it's an alternate interior angle to ∠2∠7 = 37° since it's vertical to ∠1 or since it's an alternate interior angle to ∠3∠8=143° since it's vertical to ∠2 or an alternate exterior angle to ∠4 or corresponds to ∠6
13. No; not congruent14. 64° 15. 72°16. 81°17. No, they are supplementary18. 83°19. 70°20. 171°21. No, they are complementary22. Complement = 6°, Supplement = 96°23. Multiple answers for the reasons. Some
examples:∠2 = 40° since it's vertical to a 40° angle and vertical angles are congruent∠3 = 140° since it's the supplement of ∠2∠1 = 140° since it's vertical to ∠3 or supplement of the 40° angle
24. Multiple answers for the reasons. Some examples:
∠1 = 68° since it's an alternate exterior angle to ∠5∠2 = 112° since it's supplemental to ∠1∠3 = 68° since it's vertical to ∠5 or corresponds to ∠1∠4 = 112° since it's supplemental to ∠3 and ∠5∠6 = 112° since it's supplemental to ∠5 or vertical to ∠4 or an alternate interior angle to ∠2∠7 = 68° since it's vertical to ∠1 or an alternate interior angle to ∠3∠8 = 112° since it's vertical to ∠2 or an alternate exterior angle to ∠4
25. 10 m26. 16 ft27. 16 in28. 24 m29. 31.4 cm30. 14.444m 31. 25.12 m 32. 77.244 cm 33. 15 m34. 8 π m35. 7.2π cm36. 10π m37. 31.5π cm38. r=5.25∈.39. 42 cm40. 100 m41. 18 ft42. 64 m43. 21.98 m 44. 200.96 in 45. 100.48 in 46. 25.12 ft 47. 2.1 cm48. 11 π m49. 48 π in.50. 24 π m51. 12π ft52. r=5.7∈.53. 24 cm²54. 121 m²55. 84 in²56. 108 m²57. 80 cm²58. 30 in²59. Area of a rectangle = length x width60. Area of a parallelogram = base x height61. The base and height always form a right
angle62. 11 cm
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63. 28 cm²64. 81 m²65. 50 in²66. 91 m²67. 143 cm²68. 102 m²69. Area of a rectangle = length x width70. Area of a parallelogram = base x height71. The base and height always form a right
angle72. 9 cm73. 60 ft²74. 78 m²75. 30 in²76. 84 in²77. 195 m²78. 5 in79. 90 ft²80. 91 m²81. 56 in²82. 105 in²83. 135 m²84. 10 in85. 314 m²86. 379.94 in²87. 78.5 m²88. 153.86 cm²89. 200.96 yd²90. Area of a circle = π x radius²91. 81π cm2 92. 144 π in2 93. 64 π m2 94. 100π cm2 95. 121π yd2 96. 254.34 m²97. 254.34 in²98. 50.24 m²99. 78.5 in²100. 153.86 m²101. Divide the diameter by 2 to find the
radius. Then, area of a circle = π x radius²102. 25 π cm2 103. 225 π in2 104. 64 π m2 105. 169π in2 106. 81π m2 107. 10,500 units²108. 14,300 units²109. 88 cm²
110. 85 mm²111. 12,200 units²112. 15,650 units²113. 238.3125 in²114. 58 ft²115. 28.26 in²116. 43 units²117. 40 ft²118. 42.14 cm²119. 43 units²120. 96 m²
Unit Review Answers
1. F, C, B, A, D, E 2. A
3. m∠1=m∠ 4=m∠5=m∠8=98 °m∠2=m∠6=m∠7=82 °
4. A5. C6. C7. B, C, and F 8. 12 units2
9. 24 yd.10. 27 cm2
11. 5.5 in.12. 144 tiles13. 44 cm2
14. 20 cm2
15. 8 cm16. 8 in17. 6.96 in18. 9120 in2
19. 220. No, Joe is not correct. Since 2 sides of the
shed need to have siding installed, the total area is 240 ft2, which is twice Joe’s answer. He didn’t multiply by 2.
21. A. 448 ft2
B. 394 ft2
C. $4728 22. A. $156
B. Answers will varyC. Answers will vary
23. A. 864 ft.B. 192 ft.C.$4,032
24. A. 80 ft2
B. 57.57 ft2
C. 2 bags
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