Name______
SEMESTER 1 EXAM REVIEW
Use the diagram to answer the following questions.
1. Find three points that are collinear.
2. Write three different names for line p.
3. Name a point not coplanar with M, R, and Z.
4. What is the intersection of and ?
Find the indicated length.
5. DE 6. AB
7. BD 8. CE
Find the exact distance between the two points.
9. A(2, 3) and B(5, -1) 10. C(4, -7) and D(-8, -2)
11. E(-1, 5) and F(3, 10) 12. G(7, 1) and H(5, 9)
Use the diagram to find the measure of the indicated angle. Then classify the angle.
13. ÐWSR
14. ÐTSW
15. ÐRST
16. ÐVST
Ð1 and Ð2 are complementary angles. Given the measure of Ð1, find mÐ2.
17. mÐ1 = 22° 18. mÐ1 = 89°
19. mÐ1 = 40° 20. mÐ1 = 61°
Ð3 and Ð4 are supplementary angles. Given the measure of Ð3, find mÐ4.
21. mÐ3 = 14° 22. mÐ3 = 100°
23. mÐ3 = 97° 24. mÐ3 = 53°
Use the diagram to tell whether the angles are vertical angles, a linear pair, or neither.
25. Ð1 and Ð2
26. Ð2 and Ð4
27. Ð5 and Ð7
28. Ð7 and Ð8
Classify the polygon by the number of sides.
29. 30.
31. 32.
Sketch a counterexample to disprove the conjecture.
45. Regular polygons always have an even number of sides.
46. The value of x2 is always greater than the value of x.
47. All intersecting planes form right angles.
48. Supplementary angles always form a linear pair.
Write the given statement in if-then form.
49. Band members are musicians.
50. The sum of two positive numbers is positive.
51. Two planes intersect at one line.
52. Three noncollinear points make a unique plane.
53. In an equilateral polygon, all sides are congruent.
Write each of the forms of the statement, “Calculus students are good at math.”
54. if-then form
55. converse
56. inverse
57. contrapositive
Write each of the forms of the statement, “A poet is a writer.”
58. if-then form
59. converse
60. inverse
61. contrapositive
Solve the equation and write a reason for each step.
66.
Statement / Reason3x – 7 = 20
67.
Statement / Reason2x + 5 = -17
68.
Statement / Reason4(x +3) = 28
69. Write a two column proof.
Given: Ð2 Ð3
Prove: Ð1 Ð4
70. Write a paragraph proof.
Use the diagram to list all pairs of the defined angles.
71. Vertical angles
72. Corresponding angles
73. Alternate Interior angles
74. Consecutive Interior angles
75. Alternate Exterior angles
Find the value of x.
76. 77.
78. 79.
80. 81.
82. 83.
Determine if the lines are parallel, perpendicular, or neither.
84. 85.
86. 87.
88. 89.
Find the slope of the line that passes through the given points.
90. (2, 7) (-1, -3) 91. (3, -1) (3, 4)
92. (0, 5) (-6, 12) 93. (5, 1) (-3, 1)
Tell whether the lines through the given points are parallel, perpendicular, or neither.
94. Line 1: (4, 7) (9, 10) 95. Line 1: (1, 2) (5, 4)
Line 2: (0, 4) (6, 14) Line 2: (7, 8) (9, 9)
96. Line 1: (5, 2) (9, 5) 97. Line 1: (7, -1) (7, 3)
Line 2: (3, 2) (0, 6) Line 2: (8, 2) (5, 2)
98. Line 1: (-1, 5) (5, 7) 99. Line 1: (2, 7) (8, 9)
Line 2: (8, 1) (5, 0) Line 2: (1, 1) (3, 7)
Write the slope-intercept equation of the line with the given information.
100. slope = 101. slope = 2
y-intercept = 7 through (5, 3)
102. slope = 103. through (3, 4) and (6, 5)
through (2, 7)
Graph the equation.
104. 105.
106. 107.
108. Write an equation of the line that passes through (5, 4) and is parallel to
109. Write an equation of the line that passes through (2, 8) and is parallel to
110. Write an equation of the line that passes through (3, 1) and is perpendicular to
111. Write an equation of the line that passes through (3, 8) and is perpendicular to
112. In the diagram, . Find the value of x.
113. In the diagram, . Find the value of x.
Find the value of x. Then classify the triangle by its angles.
114. 115.
116. 117.
118. 119.
120. 121.
122. 123.
In the diagram, .
124. 125.
126. 127.
128. 129.
130. 131.
132. IW = ______133.
State the congruence that is needed to prove using the given postulate or theorem.
134. Given:
using AAS
135. Given:
using ASA
136. Given:
using SAS
Decide whether the triangles can be proven congruent. If so, state the postulate or theorem and write a congruence statement.
137. 138.
139. 140.
Find the value of x.
141. 142.
143. 144.
145. 146.
Sketch the image of the figure after the translation.
147. 148.
Use coordinate notation to describe the transformation from the pre-image (solid lines) to the image (dashed lines).
149. 150.
151. 152.
is a midsegment of DLNO. Find the value of x.
153. 154.
155. 156.
Use D GHJ where D, E, and F are midpoints of the sides.
157. If DE = 4x + 5 and GJ = 3x + 25, what is DE ?
158. If EF = 2x + 7 and GH = 5x – 1, what is EF ?
159. If HJ = 8x – 2 and DF = 2x + 11, what is HJ ?
Place the figure in a coordinate plane in a convenient way. Give the coordinates of each vertex.
160. right triangle: one leg is 3 161. square: side length is 6
one leg is 5
162. rectangle: one side is twice as 163. isosceles right triangle
long as the other side
164. rectangle: one side is 2 165. right triangle: one side is 6
one side is 5 one side is half as long
In the diagram, the perpendicular bisectors of DABC meet at point G and are shown as dashed segments. Find the indicated measures.
166. AG
167. BD
168. CF
169. BG
170. CE
171. AC
Use the information in the diagram to find x.
172. 173.
174. 175.
G is the centroid of DABC, AD = 8, AG = 10, and CD = 18. Find the indicated measures.
176. BD
177. AB
178. EG
179. AE
180. CG
181. DG
Find the coordinates of the centroid P of DSTU.
182. S(-7, -4) T(-3, 5) U(1, -4) 183. S(0, -2) T(6, 1) U(9, -5)
184. S(-2, 7) T(6, 1) U(2, -5) 185. S(4, 5) T(9, 1) U(2, -3)
List the unknown sides in order from least to greatest.
186. 187.
188. 189.
List the unknown angles in order from least to greatest.
190. 191.
192. 193.
Describe the possible lengths of the third side of a triangle given the lengths of the other two sides.
194. 12 in, 6 in 195. 3 ft, 8 ft
196. 12 cm, 17 cm 197. 7 yd, 13 yd
Fill in the blank with <, >, or =.
198. ST______VW 199. ED______EF
200. JK______LM 201. AB______DC
Simplify the ratio.
202. 203.
204. 205.
Solve the proportion.
206. 207.
208. 209.
210. 211.
In the diagram, WXYZ ~ MNOP.
212. Find the scale factor of WXYZ to MNOP.
213. Find the value of x.
214. Find the value of y.
215. Find the value of z.
216. Find the perimeter of WXYZ.
217. Find the perimeter of MNOP.
In the diagram, BCDE ~ WXYZ.
218. Find the scale factor of BCDE to WXYZ.
219. Find XY.
220. Find YZ.
221. Find mÐC.
222. Find the perimeter of WXYZ.
Determine whether the triangles are similar. If so, write a similarity statement.
223. 224.
225. 226.
227. 228.
Find the value of x.
229. 230.
Find the value of x.
231. 232.
233. 234.
235. 236.
237. 238.
KEY
1. A, Z, and R
2. , , and
3. D or Q
4. A
5. 9
6. 6
7. 12
8. 15
9. 5
10. 13
11.
12. or
13. 65° acute
14. 115° obtuse
15. 180° straight
16. 90° right
17. 68°
18. 1°
19. 50°
20. 29°
21. 166°
22. 80°
23. 83°
24. 127°
25. linear pair
26. vertical angles
27. neither
28. linear pair
29. hexagon
30. octagon
31. pentagon
32. decagon
33. 42 ft
34. in
35. 16p m
36. 6p ft
37. 90 ft2
38. in2
39. 64p m2
40. 9p ft2
41.
42.
43. 10, 15, 21
44. 360, 2160, 15120
45-48. answers will vary
49. If you are in band, then you are a musician.
50. If there are two positive numbers, then their sum is positive.
51. If two planes intersect, then their intersection is a line.
52. If three points are noncollinear, then they are in one plane.
53. If a polynomial is equilateral, then its sides are congruent.
54. If you are in calculus, then you are good at math.
55. If you are good at math, then you are in calculus.
56. If you aren’t in calculus, then you aren’t good at math.
57. If you aren’t good at math, then you aren’t in calculus.
58. If you are a poet, then you are a writer.
59. If you are a writer, then you are a poet.
60. If you aren’t a poet, then you aren’t a writer.
61. If you aren’t a writer, then you aren’t a poet.
62. Someone is home.
63. You can take the test.
64. If Celia practices all week, then the team will win.
65. If 5x = 65, then x2 = 169.
66-70. Answers will vary
71. Ð1&Ð4
Ð2&Ð3
Ð5&Ð8
Ð6&Ð7
72. Ð1&Ð5
Ð2&Ð6
Ð3&Ð7
Ð4&Ð8
73. Ð3&Ð6
Ð4&Ð5
74. Ð3&Ð5
Ð4&Ð6
75. Ð1&Ð8
Ð2&Ð7
76. x = 25
77. x = 33
78. x = 16
79. x = 60
80. x = 130
81. x = 70
82. x = 60
83. x = 4
84. neither
85. parallel
86. perpendicular
87. neither
88. parallel
89. perpendicular
90.
91. no slope
92.
93. 0
94. neither
95. parallel
96. perpendicular
97. perpendicular
98. parallel
99. neither
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112. x = 15
113. x = 7
114. x = 20, acute
115. x = 60, equiangular
116. x = 51, acute
117. x = 26, acute
118. x = 12, right
119. x = 10, right
120. x = 30, right
121. x = 23, acute
122. x = 25, acute
123. x = 22, acute
124.
125. ÐL
126. ÐG
127.
128. 55°
129. 92°
130. 33°
131. 33°
132. 4 cm
133.
134. or
135.
136.
137. No
138. Yes
139. No
140. Yes
141. x = 12
142. x = 4
143. x = 8
144. x = 5
145. x = 6.75
146. x = 7
147.
148.
149. (x, y) ® (x – 4, y + 1)
150. (x, y) ® (x + 4, y – 4)
151. (x, y) ® (x + 12, y – 10)
152. (x, y) ® (x + 3, y – 4)
153. x = 8
154. x = 14
155. x = 4
156. x = 9
157. 17
158. 37
159. 46
160. (0,0) (0,5) (3,0)
or
(0,0) (5,0) (0,3)
161. (0,0) (6,0) (0,6) (6,6)
162. (0,0) (0,a) (2a,0) (2a, a)
or
(0,0) (a, 0) (0, 2a) (a, 2a)
163. (0, 0) (a, 0) (0, a)
164. (0, 0) (5, 0) (0, 2) (5, 2)
or
(0, 0) (0, 5) (2, 0) (2, 5)
165. (0, 0) (3, 0) (0, 6)
or
(0, 0) (0, 3) (6, 0)
166. 25
167. 20
168. 24
169. 25
170. 15
171. 48
172. x = 11
173. x = 8
174. x = 7
175. x = 3
176. 8
177. 16
178. 5
179. 15
180. 12
181. 6
182. (-3, -1)
183. (5, -2)
184. (2, 1)
185. (5, 1)
186.
187.
188.
189.
190. ÐE, ÐD, ÐF
191. ÐR, ÐS, ÐT
192. ÐB, ÐC, ÐA
193. ÐC, ÐA, ÐB
194. 6 < x < 18
195. 5 < x < 11
196. 5 < x < 29
197. 6 < x < 20
198.
199.
200.
201. =
202.
203.
204.
205.
206.
207.
208. x = 7.2
209. x = 6.5
210. x = 3
211.
212. 8:10 or 4:5
213. x = 15
214. y = 8
215. z = 135
216. 40
217. 50
218. 4:6 or 2:3
219. 4.5
220. 9
221. 117°
222. 24
223. yes
DABC ~ DFDE
224. no
225. no
226. yes
DABC ~ DDEF
or
DABC ~ DEDF
227. yes
DRST ~ DQSU
228. yes
DRST ~ DXYZ
229. x = 6
230. x = 10
231. x = 7.5
232.
233. x = 21
234.
235.
236. x = 34
237. x = 21
238. x = 15
vertices at the following points:
239. (2, 4) (6, -4) (-2, 0)
240. (0, 3) (4, 1) (-5, -4)
241. (3, 3) (6, -6) (-3, 6)
242. (0, 6) (3, 0) (-3, -6)
243. (0, 0) (6, -4) (-4, -2)
244. (1, -1) (1, 2) (-2, 1)
245. (3, 3) (-6, -6) (-6, 6)
246. (6, 4) (2, -6) (0, 2)