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Name: _____________________________________________________Geometry Summer Packet
Welcome to the study of Geometry! You have an opportunity this summer to help strengthen your skills. Please read
the information below carefully. Also, please note that this packet is mandatory for Pre-AICE Geometry & Geometry
Honors students. It will be counted as extra credit for standard Geometry (no honors designation) students.
Keep your packet in a folder that has clips (duo-tang folder). Your work should be neat and legible. Show all work on the
hand-out. Purple Math is a great site and will provide you with examples and lessons to help you complete assignments.
You can also search topics in Google or YouTube for other help. Don’t buy anything; there is plenty of free help out there
on the web.
****Remember that in every mathematics class, showing all work completely for every problem is a requirement. Not
showing your work in mathematics is similar to not writing your Language Arts assignments in complete sentences. ****
You will need the following materials starting your very first day:
Geometry summer packet
loose leaf paper
graph paper
pencils
erasers
calculator
any other materials on your teacher’s syllabus
The booklet containing your packet should be ready to turn in the first day of class. Come to class prepared to start
working! A scientific calculator is a must for geometry. Please purchase one of the five following calculators that are
approved to use on the Geometry FSA:
Texas Instruments TI-30Xa
Casio fx-260 solar
Casio fx-82 solar
Sharp EL-510R
Sharp EL-510RN
NOTE: These will be the only calculators you will be permitted to use in Geometry this year.
The geometry teachers look forward to seeing you next August!
Topic 1: Simplifying Square Roots (Remember to show all work & all calculations)
# 1 – 12: Simplify each radical by hand.
1. √96
2. √216
3. √98
4. √18
5. √72
6. √144
7. √45
8. √175
9. √343
10. √12
11. 10√96
12. 9√245
Topic 2: Classifying Angles ______ (Remember to show all work & all calculations)
# 13 – 40: Classify each angle as acute, obtuse, right, or straight.
13.
14. 15.
16. 17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27. Angle measuring 16°
28. Angle measuring 180° 29. Angle measuring 90° 30. Angle measuring 97°
31. Angle measuring 59° 32. Angle measuring 39° 33. Angle measuring 119°
34. Angle measuring 82° 35. Angle measuring 162° 36. Angle measuring 52°
37. Angle measuring 15° 38. Angle measuring 116° 39. Angle measuring 96° 40. Angle measuring 74°
Topic 3: The Midpoint Formula ______ (Remember to show all work & all calculations)
# 41 – 44: Find the midpoint of each line segment.
41. 42.
43. 44.
# 45 – 50: Find the midpoint of the line segment with the given endpoints.
45. (-4, 4) and (5, -1)
46. (2, 4) and (1, -3)
47. (5, 2) and (-4, -3)
48. (2, -1) and (-6, 0)
49. (-5.1, -2) and (1.4, 1.7)
50. (5.1, -2) and (6, 3.6)
# 51 – 53: Find the other endpoint of the line segment with the given endpoint and midpoint.
51. Endpoint: (-1, 9); midpoint: (-9, -10)
52. Endpoint: (5, 2); midpoint: (-10, -2)
53. Endpoint: (-9, 7); midpoint: (10, -3)
54. Find the point that is one-fourth of the way
from (2, 4) to (10, 8)
Topic 4: Solving Proportions ______ ___ (Remember to show all work & all calculations)
# 55 – 58: Solve each proportion. Leave your answer as a fraction in simplest form.
55. 6
2=
4
𝑝
56. 𝑛
4=
8
7
57. 𝑚
5=
7
2
58. 7
6=
5
𝑥
# 59 – 60: Solve each proportion. Round your answers to the nearest hundredth.
59. 7.7
3.6=
2.3
𝑏
60. 6.3
𝑥=
2.56
9.3
# 61 – 66: Solve each proportion. Leave your answer as a fraction in simplest form.
61. 9
8=
𝑘+6
6
62. 10
𝑝+2=
4
3
63. 𝑚
8=
𝑚+7
9
64. 9
4=
𝑟−10
𝑟
65. 𝑛−9
𝑛+5=
7
4
66. 8
3=
𝑣−9
7𝑣+4
Topic 5: Circumference and Area of Circles _____ (Remember to show all work & all calculations)
# 67 – 74: Find the area of each. Use your calculator’s value of π. Round your answer to the nearest tenth.
67. 68.
69. 70.
71. Radius = 2.6 in
72. Radius = 34.1 in
73. Radius = 12.3 km
74. Radius = 29.9 km
# 75 – 82: Find the circumference of each circle. Use your calculator’s value of π. Round your answer to the nearest
tenth.
75.
76.
77.
78.
79. Radius = 5.2 ft
80. Radius = 11.1 ft
81. Radius = 9.5 in
82. Radius = 9.3 in
# 83 – 86: Find the radius of each circle. Use your calculator’s value of π. Round your answer to the nearest tenth.
83. Circumference = 62.8 mi
84. Circumference = 69.1 yd
85. Circumference = 12.6 yd
86. Circumference = 25.1 ft
# 87 & 88: Find the diameter of each circle. Use your calculator’s value of π. Round your answer to the nearest tenth.
87. Area = 201.1 in2
88. Area = 78.5 ft2
# 89 & 90: Find the circumference of each circle.
89. Area = 64π mi2
90. Area = 16π in2
# 91 & 92: Find the area of each circle.
91. Circumference = 6π yd
92. Circumference = 22π in
Topic 6: The Distance Formula ______ _ (Remember to show all work & all calculations)
# 93 – 104: Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.
93.
94.
95.
96. (-2, 3) and (-7, -7)
97. (5, 9) and (-7, -7)
98. (-10, -7) and (-8, 1)
99.
100.
101.
102. (0, -2) and (-5, -1)
103. (3, 8) and (9, 10)
104. (-8, 10) and (-6, 7)
Topic 7: Graphing Lines ______ _______ (Remember to show all work & all calculations)
# 105 – 116: Sketch the graph of each line.
105. 𝑦 = 7
2𝑥 − 2
106. 𝑦 = −6𝑥 + 3
107. 𝑦 = −5
108. 𝑦 = 6
5𝑥 + 1
109. 𝑦 =1
4𝑥 + 2
110. 𝑥 = 5
111. 𝑦 = 5
3𝑥
112. 𝑥 = 0
113. 𝑦 = −1
3𝑥 + 3
114. 𝑦 = 1
5𝑥 − 4
115. 𝑦 =1
2𝑥 − 2
116. 𝑦 = 2𝑥 + 5
Topic 8: Multi-Step Equations ______ _ (Remember to show all work & all calculations)
# 117 – 136: Solve each equation.
117. −20 = −4𝑥 − 6𝑥
118. 6 = 1 − 2𝑛 + 5
119. 8𝑥 − 2 = −9 + 7𝑥
120. 𝑎 + 5 = −5𝑎 + 5
121. 4𝑚 − 4 = 4𝑚
122. 𝑝 − 1 = 5𝑝 + 3𝑝 − 8
123. 5𝑝 − 14 = 8𝑝 + 4
124. 𝑝 − 4 = −9 + 𝑝
125. −8 = −(𝑥 + 4)
126. 12 = −4(−6𝑥 − 3)
127. 14 = −(𝑝 − 8)
128. −(7 − 4𝑥) = 9
129. −18 − 6𝑘 = 6(1 + 3𝑘)
130. 5𝑛 + 34 = −2(1 − 7𝑛)
131. 2(4𝑥 − 3) − 8 = 4 + 2𝑥
132. 3𝑛 − 5 = −8(6 + 5𝑛)
133. −(1 + 7𝑥) − 6(−7 − 𝑥) = 36
134. −3(4𝑥 + 3) + 4(6𝑥 + 1) = 43
135. 24𝑎 − 22 = −4(1 − 6𝑎)
136. −5(1 − 5𝑥) + 5(−8𝑥 − 2) = −4𝑥 − 8𝑥
Topic 9: Area of Triangles and Quadrilaterals ____ _____ (Remember to show all work & all calculations)
# 137 – 156: Find the area of each.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154. 155.
Topic 10: Finding Slope from Two Points ______ (Remember to show all work & all calculations)
# 157 – 164: Find the slope of the line through each pair of points.
156. (19, -16) and (-7, -15)
157. (-4, 7) and (-6, -4)
158. (17, -13) and (17, 8)
159. (3, 0) and (-11, -15)
160. (6, -10) and (-15, 15)
161. (3, -20) and (5, 8)
162. (-19, 12) and (-9, 1)
163. (6, -12) and (15, -2)
