GEOMETRY: STUDY GUIDE FOR SEMESTER EXAM



GEOMETRY: STUDY GUIDE FOR SEMESTER EXAM

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

1. Which angle is an obtuse angle?

a. [pic] b. [pic] c. [pic] d. [pic]

2. Which angles are corresponding angles?

[pic]

a. [pic]

b. [pic]

c. [pic]

d. none of these

3. Which statement is true?

[pic]

a. [pic]are same-side interior angles.

b. [pic]are alternate angles.

c. [pic]are alternate angles.

d. [pic]are same-side interior angles.

4. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.

a. [pic] b. [pic] c. [pic] d. [pic]

5. Write an equation for the horizontal line that contains point E(–7, 6).

a. y = 6 b. y = –7 c. x = –7 d. x = 6

6. Write an equation in slope-intercept form of the line through point P(–1, –10) with slope 5.

a. y + 10 = 5(x + 1) b. y = 5x – 5 c. y + 1 = 5(x + 10) d. y = 5x – 10

7. Write an equation in slope-intercept form of the line through points S(–2, –1) and T(8, 7).

a. y = [pic]x + [pic] b. y = [pic]x – [pic] c. [pic] [pic]x – [pic] d. [pic] [pic]x + [pic]

8. Which two lines are parallel?

| |I. |[pic] |

| |II. |[pic] |

| |III. |[pic] |

a. II and III b. I and III c. I and II d. No two of the lines are parallel.

9. If [pic], which of the following can you NOT conclude as being true?

a. [pic] b. [pic] c. [pic] d. [pic]

10. The length of [pic] is shown. What other length can you determine for this diagram?

[pic]

a. EF = 15

b. DG = 15

c. DF = 30

d. No other length can be determined.

11. Name the smallest angle of [pic] The diagram is not to scale.

[pic]

a. [pic]

b. Two angles are the same size and smaller than the third.

c. [pic]

d. [pic]

12. Which three lengths could be the lengths of the sides of a triangle?

a. 6 cm, 22 cm, 12 cm b. 12 cm, 5 cm, 17 cm c. 21 cm, 5 cm, 10 cm d. 10 cm, 14 cm, 22 cm

13. Which three lengths can NOT be the lengths of the sides of a triangle?

a. 17 m, 5 m, 10 m b. 7 m, 10 m, 5 m c. 10 m, 14 m, 12 m d. 22 m, 20 m, 15 m

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

14. [pic]

a. 133

b. 11.53

c. 9.17

d. 15.1

Short Answer

15. If BCDE is congruent to OPQR, then [pic] is congruent to [pic]

16. [pic]

17. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to scale.

18. Given [pic] [pic] and [pic], find the length of QS and TV.

19. Given [pic] [pic] and [pic], find [pic] and [pic]

20. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 54°?

21. Use the information in the figure. Find [pic]

22. Find the value of x. The diagram is not to scale.

[pic]

23. Find the value of x. The diagram is not to scale.

[pic]

24. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

[pic]

25. Find the value of x.

[pic]

26. Find the length of the midsegment. The diagram is not to scale.

[pic]

27. Q is equidistant from the sides of [pic] Find the value of x. The diagram is not to scale.

[pic]

28. Q is equidistant from the sides of [pic] Find [pic] The diagram is not to scale.

[pic]

29. Find the center of the circle that you can circumscribe about the triangle.

[pic]

30. In DABC, G is the centroid and BE = 12. Find BG and GE.

[pic]

31. Name a median for [pic]

[pic]

32. In [pic] centroid D is on median [pic]. [pic] and [pic] Find AM.

33. List the sides in order from shortest to longest. The diagram is not to scale.

[pic]

34. Find the values of the variables and the lengths of the sides of this kite.

[pic]

35. ABCD is a parallelogram. If [pic] then [pic] The diagram is not to scale.

[pic]

36. ABCD is a parallelogram. If [pic] then [pic] The diagram is not to scale.

[pic]

37. LMNO is a parallelogram. If NM = x + 35 and OL = 5x + 7 find the value of x and then find NM and OL.

[pic]

38. For the parallelogram, if [pic] and [pic] find [pic] The diagram is not to scale.

[pic]

39. Find the values of the variables in the parallelogram. The diagram is not to scale.

[pic]

40. In parallelogram DEFG, DH = x + 4, HF = 2y, GH = 2x – 4, and HE = 3y + 4. Find the values of x and y. The diagram is not to scale.

[pic]

41. In the figure, the horizontal lines are parallel and [pic] Find KL and FG. The diagram is not to scale.

[pic]

42. Find AM in the parallelogram if PN =14 and AO = 6. The diagram is not to scale.

[pic]

43. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to

scale.

[pic]

44. In the rhombus, [pic] Find the value of each variable. The diagram is not to scale.

[pic]

45. DEFG is a rectangle. DF = 6x – 1 and EG = x + 59. Find the value of x and the length of each diagonal.

46. Find the values of a and b.The diagram is not to scale.

[pic]

47. Find [pic] in the kite. The diagram is not to scale.

[pic]

48. One side of a kite is 6 cm less than four times the length of another side. The perimeter of the kite is 69 cm. Find the lengths of the sides of the kite.

Find the area. The figure is not drawn to scale.

49. [pic]

50. [pic]

51.

[pic]

52. [pic]

53. [pic]

54. Find the value of h in the parallelogram.

[pic]

Not drawn to scale

Find the length of the missing side. The triangle is not drawn to scale.

55. [pic]

56. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.

57. A triangle has side lengths of 6 cm, 8 cm, and 9 cm. Classify it as acute, obtuse, or right.

58. Find the length of the hypotenuse.

[pic]

59. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

[pic]

60. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.

[pic]

61. The area of a square garden is 200 m2. How long is the diagonal?

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

62. [pic]

63. [pic]

Not drawn to scale

64. Find the value of x and y rounded to the nearest tenth.

[pic]

Find the area of the trapezoid. Leave your answer in simplest radical form.

65. A kite has diagonals 3.2 ft and 9 ft. What is the area of the kite?

66. Find the area of the rhombus.

[pic]

67. Find the area of the rhombus. Leave your answer in simplest radical form.

[pic]

68. Find the area of a regular hexagon with an apothem 13.9 feet long and a side 16 feet long. Round your answer to the nearest tenth.

69. Find the area of an equilateral triangle with side 12.

70. Find the length of arc XPY. Leave your answer in terms of [pic].

[pic]

71. Find the area of the figure to the nearest tenth.

[pic]

72. Find the exact area of the shaded region.

[pic]

73. A model is made of a car. The car is 7 feet long and the model is 7 inches long. What is the ratio of the length of the car to the length of the model?

Solve the proportion.

74. [pic]

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

75. In DRST, RS = 10, RT = 15, and mÐR = 32. In DUVW, UV = 12, UW = 18, and mÐU = 32.

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.

76. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

[pic]

77. Use the information in the diagram to determine the height of the tree to the nearest foot.

[pic]

78. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

[pic]

Solve for a and b.

79. [pic]

80. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

[pic]

81. Use the Side-Splitter Theorem to find x, given that [pic].

[pic]

Solve for x.

82. [pic]

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.

83. The area of the larger triangle is 1215 ft[pic].

[pic]

84. Find the similarity ratio and the ratio of perimeters for two regular octagons with areas of [pic] and [pic].

Find the value of x. Round your answer to the nearest tenth.

85. [pic]

86. [pic]

87. [pic]

Find the value of x to the nearest degree.

88. [pic]

89. Find the missing value to the nearest tenth.

[pic]

90. Viola drives 2 kilometers up a hill that makes an angle of 8[pic] with the horizontal. To the nearest tenth of a kilometer, what horizontal distance has she covered?

91. An airplane over the Pacific sights an atoll at an angle of depression of 5[pic]. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?

[pic]

92. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.

93. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number.

[pic]

94. The radius of the base of a cylinder is 36 mm and its height is 43 mm. Find the surface area of the cylinder in terms of [pic].

Find the surface area of the pyramid shown to the nearest whole number.

95. [pic]

96. Find the slant height x of the pyramid shown to the nearest tenth.

[pic]

97. Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.

98. Find the surface area of the cone in terms of [pic].

[pic]

99. The lateral area of a cone is 164[pic] cm[pic]. The radius is 41 cm. Find the slant height to the nearest tenth.

Find the volume of the given prism. Round to the nearest tenth if necessary.

100. [pic]

101. [pic]

Find the volume of the cylinder in terms of [pic].

102. [pic]

103. Find the volume of the composite space figure to the nearest whole number.

[pic]

Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.

104. [pic]

Find the volume of the cone shown as a decimal rounded to the nearest tenth.

105. [pic]

Find the surface area of the sphere with the given dimension. Leave your answer in terms of [pic].

106. diameter of 20 cm

107. The volume of a sphere is 5000[pic] m[pic]. What is the surface area of the sphere to the nearest square meter?

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

108. [pic] 142

[pic]

109. [pic] 24

[pic]

110. [pic] is tangent to circle A at B and to circle D at C (not drawn to scale).

AB = 9, BC = 21, and DC = 3. Find AD to the nearest tenth.

[pic]

111. [pic] is tangent to circle O at B. Find the length of the radius r for AB = 7 and AO = 7.4. Round to the nearest tenth if necessary. The diagram is not to scale.

[pic]

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

112. [pic], [pic], FG = 40, RS = 28, OP = 18

[pic]

113. [pic]

114. [pic]

115. [pic]

116. The figure consists of a chord, a secant and a tangent to the circle. Round to the nearest hundredth, if necessary.

[pic]

117. AB = 18, BC = 8, and CD = 6

[pic]

118. The radius of circle O is 18, and OC = 8. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.)

[pic]

119. Find m[pic]BAC. (The figure is not drawn to scale.)

[pic]

120. [pic] is tangent to circle O at C, m(arc AEC) = 292, and m[pic]ACE = 72. Find m[pic]DCE.

(The figure is not drawn to scale.)

[pic]

121. If m(arc BY) = 48, what is m[pic]YAC? (The figure is not drawn to scale.)

[pic]

122. In the circle, m(arc AD) = 92, and m[pic]D = 92. Find m[pic]DCQ.

(The figure is not drawn to scale.)

[pic]

123. m(arc DE) = 128 and m(arc BC) = 52. Find m[pic]A. (The figure is not drawn to scale.)

[pic]

124. Find the value of x for m(arc AB) = 47 and m(arc CD) = 23. (The figure is not drawn to scale.)

[pic]

125. Find m[pic]D for m[pic]B = 58. (The figure is not drawn to scale.)

[pic]

126. m[pic]S = 44, m(arc RS) = 112, and [pic] is tangent to the circle at R. Find m[pic]U.

(The figure is not drawn to scale.)

[pic]

127. A park maintenance person stands 16 m from a circular monument. If you assume her lines of sight form tangents to the monument and make an angle of 37°, what is the measure of the arc of the monument that her lines of sight intersect?

128. Find the diameter of the circle for BC = 10 and DC = 29. Round to the nearest tenth.

(The diagram is not drawn to scale.)

[pic]

129. Find AB. Round to the nearest tenth if necessary.

[pic]

130. A footbridge is in the shape of an arc of a circle. The bridge is 6 ft tall and 15 ft wide. What is the radius of the circle that contains the bridge? Round to the nearest tenth.

Write the standard equation for the circle.

131. center (–9, –6), r = 10

132. center (–6, –8), that passes through (0, 0)

133. Find the center and radius of the circle with equation (x + 10)[pic] + (y – 7)[pic] = 49.

134. Line r is parallel to line t. Find m[pic]5. The diagram is not to scale.

[pic]

135. Find the value of the variable if [pic] [pic] and [pic] The diagram is not to scale.

[pic]

136. Find the values of x and y. The diagram is not to scale.

[pic]

137. Find [pic] The diagram is not to scale.

[pic]

138. Find the value of k. The diagram is not to scale.

[pic]

139. Find the values of x, y, and z. The diagram is not to scale.

[pic]

140. Classify the triangle by its sides. The diagram is not to scale.

[pic]

141. Classify [pic]ABC by its angles, when m[pic]A = 26, m[pic]B = 86, and m[pic]C = 68.

142. Find the value of x. The diagram is not to scale.

[pic]

143. Find the value of the variable. The diagram is not to scale.

[pic]

144. Classify the polygon by its sides.

[pic]

145. Find the sum of the measures of the angles of the figure.

[pic]

146. How many sides does a regular polygon have if each exterior angle measures 30?

147. Find [pic]. The diagram is not to scale.

[pic]

148. Based on the pattern, what are the next two terms of the sequence?

5, 14, 23, 32, . . .

149. Find a counterexample to show that the conjecture is false.

Conjecture: Any number that is divisible by 6 is also divisible by 12.

150. Are E, F, and H collinear? If so, name the line on which they lie.

[pic]

151. Name the plane represented by the top of the box.

[pic]

152. What is the intersection of plane TUYX and plane VUYZ?

[pic]

153. Name the ray in the figure.

[pic]

154. Name the four labeled segments that are skew to [pic]

[pic]

155. Name the three labeled segments that are parallel to [pic]

[pic]

156. Which plane is parallel to plane BDHF?

[pic]

157. Find AC.

[pic]

158. If [pic] find the values of x, EF, and FG. The drawing is not to scale.

[pic]

159. If T is the midpoint of [pic] find the values of x and ST. The diagram is not to scale.

[pic]

160. Which point is the midpoint of [pic]?

[pic]

161. If [pic] and [pic], then what is the measure of [pic] The diagram is not to scale.

[pic]

162. If [pic] and [pic] then what is the measure of [pic] The diagram is not to scale.

[pic]

163. If [pic] then what are [pic] and [pic] The diagram is not to scale.

[pic]

164. [pic] bisects [pic] [pic] and [pic] Solve for x and find [pic] The diagram is not to scale.

[pic]

165. [pic] bisects [pic], [pic], [pic]. Find [pic]. The diagram is not to scale.

[pic]

166. [pic] bisects [pic], and [pic]. Write an expression for [pic]. The diagram is not to scale.

[pic]

167. Find the distance between points P(7, 7) and Q(9, 3) to the nearest tenth.

168. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 10) and K(8, 14).

169. M(4, 5) is the midpoint of [pic] The coordinates of S are (6, 6). What are the coordinates of R?

170. Ross wants to put a fence around his rectangular garden. His garden measures 33 feet by 46 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Ross need to enclose the garden and path?

171. Find the circumference of the circle in terms of p.

[pic]

172. Find the area of the circle in terms of p.

[pic]

173. The figure is formed from rectangles. Find the total area. The diagram is not to scale.

[pic]

174. If the perimeter of a square is 124 inches, what is its area?

175. Write an expression that gives the area of the shaded region in the figure below. You do not have to evaluate the expression. The diagram is not to scale.

[pic]

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