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 AQ and ZR ?

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. ∠WSR

14. ∠TSW

15. ∠RST

16. ∠VST

∠1 and ∠2 are complementary angles. Given the measure of ∠1, find m∠2.

17. m∠1 = 22° 18. m∠1 = 89°

19. m∠1 = 40° 20. m∠1 = 61°

∠3 and ∠4 are supplementary angles. Given the measure of ∠3, find m∠4.

21. m∠3 = 14° 22. m∠3 = 100°

23. m∠3 = 97° 24. m∠3 = 53°

Use the diagram to tell whether the angles are vertical angles, a linear pair, or neither.

25. ∠1 and ∠2

26. ∠2 and ∠4

27. ∠5 and ∠7

28. ∠7 and ∠8

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.

67.

68.

Statement Reason

3x – 7 = 20

Statement Reason

2x + 5 = -17

Statement Reason

4(x +3) = 28

69. Write a two column proof.

Given: ∠2 ≅ ∠3

Prove: ∠1 ≅ ∠4

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. 432 += xy 85. 63 −= xy

523−= xy 13 += xy

86. 102 += xy 87. 82 +−= xy

221 +−= xy 72 −= xy

88. 352 −= xy 89. 113 +−= xy

152 += xy 9

31 += xy

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 = 32 101. slope = 2

y-intercept = 7 through (5, 3)

102. slope = 21 103. through (3, 4) and (6, 5)

through (2, 7)

Graph the equation.

104. 232 +−= xy 105. 43 −= xy

106. 321 −= xy 107. xy =

108. Write an equation of the line that passes through (5, 4) and is parallel to

72 −= xy

109. Write an equation of the line that passes through (2, 8) and is parallel to

1121 += xy

110. Write an equation of the line that passes through (3, 1) and is perpendicular to

1021 += xy

111. Write an equation of the line that passes through (3, 8) and is perpendicular to

523−−= xy

112. In the diagram, FGCD ⊥ . Find the value of x.

113. In the diagram, BCAB ⊥ . 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, GIWALX ∆≅∆ .

124. __________≅LX 125. __________≅∠I

126. __________≅∠A 127. __________≅WG

128. __________=∠Am 129. __________=∠Wm

130. __________=∠Im 131. __________=∠Lm

132. IW = __________ 133. __________≅∆LAX

State the congruence that is needed to prove QRTDEF ∆≅∆ using the given postulate or

theorem.

134. Given: TFQD ∠≅∠∠≅∠ ,

using AAS

135. Given: RTEFRE ≅∠≅∠ ,

using ASA

136. Given: QDQRDE ∠≅∠≅ ,

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. )1,5(),( +−→ yxyx 148. )2,5(),( −+→ yxyx

Use coordinate notation to describe the transformation from the pre-image (solid lines) to

the image (dashed lines).

149. 150.

151. 152.

MP is a midsegment of ∆LNO. Find the value of x.

153. 154.

155. 156.

Use ∆ 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 ∆ABC 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 ∆ABC, 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 ∆STU.

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. m

m

6

15 203.

in

in

24

22

204. ft

in

2

14 205.

m

cm

2

500

Solve the proportion.

206. 3

2

14=

x 207.

x

10

5

3=

208. 8

4

5

2 −=

x 209.

10

8

1

6=

+x

210. 2

1

6

32=

−x 211.

8

13

10

9 +=

x

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 m∠C.

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. AZ , AR , and ZR

3. D or Q

4. A

5. 9

6. 6

7. 12

8. 15

9. 5

10. 13

11. 41

12. 68 or 172

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. 411 in

35. 16π m

36. 6π ft

37. 90 ft2

38. 181 in2

39. 64π m2

40. 9π 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. ∠1&∠4

∠2&∠3

∠5&∠8

∠6&∠7

72. ∠1&∠5

∠2&∠6

∠3&∠7

∠4&∠8

73. ∠3&∠6

∠4&∠5

74. ∠3&∠5

∠4&∠6

75. ∠1&∠8

∠2&∠7

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. 3

10

91. no slope

92. 67

−

93. 0

94. neither

95. parallel

96. perpendicular

97. perpendicular

98. parallel

99. neither

100. 732 += xy

101. 72 −= xy

102. 621 += xy

103. 331 += xy

104.

105.

106.

107.

108. 62 −= xy

109. 721 += xy

110. 72 +−= xy

111. 632 += xy

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. IW

125. ∠L

126. ∠G

127. XA

128. 55°

129. 92°

130. 33°

131. 33°

132. 4 cm

133. IGW∆

134. RTEF ≅ or RQED ≅

135. TF ∠≅∠

136. QTDF ≅

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. XZYZXY ,,

187. KLJLJK ,,

188. BCABAC ,,

189. DEEFDF ,,

190. ∠E, ∠D, ∠F

191. ∠R, ∠S, ∠T

192. ∠B, ∠C, ∠A

193. ∠C, ∠A, ∠B

194. 6 < x < 18

195. 5 < x < 11

196. 5 < x < 29

197. 6 < x < 20

198. >

199. <

200. <

201. =

202. 25

203. 1211

204. 127

205. 25

206. 3.9=x

207. 6.16=x

208. x = 7.2

209. x = 6.5

210. x = 3

211. 60.2=x

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

∆ABC ~ ∆FDE

224. no

225. no

226. yes

∆ABC ~ ∆DEF

or

∆ABC ~ ∆EDF

227. yes

∆RST ~ ∆QSU

228. yes

∆RST ~ ∆XYZ

229. x = 6

230. x = 10

231. x = 7.5

232. 71.7≈x

233. x = 21

234. 3.3=x

235. 3.2=x

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)