Geometry Semester Review 2 Semester

Semester Review – 2nd Semester

Geometry Semester Review – 2nd Semester

Directions with an ‘*’ must be left in radical form. MUST SHOW WORK ON ALL PROBLEMS!

*1-4. Solve for the each variable.

1. 2.

3. 4.

*4-6. Simplify. *7-9. Classify the triangle as acute, right, or obtuse.

4. √8 ∙√96

√18 7. 20, 21, 28

5. (2√48)(3√80) 8. 11, 22,34

6. 4√125∙√20

3√96 9. 2√67, 16, 28


*10-17. Solve for each variable below.

10. 11.

12. 13.

14. 15.

16. 17.


18-25. Solve for each variable below.

18. 19.

20. 21.

22. 23.

24. 25.


26. A man is standing at the top of a 100 foot cliff looking down at a 45° angle onto a lake, where he sees a speed boat. If

he measured the distance between him and the boat, how far would it be?

27. An airplane is 13,200 feet off the ground. To land at an airport up ahead, the pilot has to travel down at an angle of

37° to reach the ground in time. What is the distance on the ground between the plane and airport?

28. You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. What angle does the ladder

make with the ground?

29. You are standing 350 feet away from a skyscraper that is 750 feet tall. What is the angle of elevation from you to the

top of the building?

Find the value of x.

31. 32.


33. The measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find

the measure of each angle.

Find the value of each variable in the parallelogram.

34. 35.

Three of the vertices of parallelogram JKLM are given. Find the coordinates of point M.

36. J(–3, 2), K(4, 2), L(2, 4), M(x, y)

Use the diagram of MNOP. Points Q, R, S, and T are midpoints of 𝑴𝑿̅̅ ̅̅ ̅, 𝑵𝑿̅̅̅̅̅, 𝑶𝑿̅̅ ̅̅ , and 𝑷𝑿̅̅ ̅̅ .

Find the indicated measure.

37. PN 41. mNXO

38. MQ 42. mMNP

39. XO 43. mNPO

40. mNMQ 44. mNOP


45. Find the value of x. 46. PQRS is a kite. Find mQ.

Give the most specific name for the quadrilateral.

47. 48.

Points D, E, F, and G are the vertices of a quadrilateral. Give the most specific name for DEFG.

49. D(0, 9), E(9, 0), F(0, –9), G(–9, 0) 50. D(–2, 5), E(3, 6), F(7, 2), G(–3, 0)

51. Three vaulting boxes used by a gymnastics team are stacked on top of each other as shown. The sides are in the shape

of a trapezoid. Find the lengths of a and b.


Find the image matrix that represents the polygon shown after a reflection in the given line.

52. y = –x 53. y = 1

Rotate the figure the given number of degrees counterclockwise about the origin. List the coordinates of the

vertices of the image.

54. 180° 55. 270°

Quadrilateral A’B’C’D’ is the image of ABCD after a translation. Write a vector for the translation.

56. 57.

The vertices of quadrilateral DEFG are D(–3, 0), E(–2, –1), F(–2, –3), and G(–4, –1). Translate DEFG using the

given vector. Graph DEFG and its image and label the vertices.

58. ⟨2, 3⟩ 59. ⟨–1, –2⟩


Add, subtract, or multiply.

60. 2.7 5.2 0.9 4.6

3.8 10.4 5.7 3.3

61.

3 2 1 0

1 6 7 4

62. 7 3 2 6

4 4 3 2

63.

3 6 4 5

8 5 1 0 7

2 1 1 1

Find the image matrix that represents the polygon shown after a reflection in the given line.

64. x-axis 65. y = x

66. a. How many lines of reflection symmetry does the figure shown have?

b. How many fold rotation symmetric is the figure?

Simplify the product.

67.

1 7

2 3 1 0

8 13


The vertices of ΔPQR are P(–4, 3), Q(–1, 4), and R(–2, –1). Find the vertices of P”Q”R” after a composition of the

transformations in the order they are listed.

68. Translation: (x, y) → (x + 3, y + 1)

Dilation: centered at the origin with k = 2

69. Dilation: centered at the origin with k = 3

Reflection: in the y-axis

Graph the equation.

70. (x - 2)2 + (y + 3)2 = 4 71. (x + 1)2 + y2 = 16


𝑩𝑫̅̅̅̅̅ and 𝑨𝑪̅̅ ̅̅ are diameters of circle F. Identify the given arc as a major arc, minor arc, or semicircle. Then find the

measure of the arc.

72. m AB 73. m BC 74. m ABC

75. m AE 76. m ACE 77. m BDC

QR is a radius of circle R and PQ is tangent to circle R. Find the value of x.

78. 79. 80.

Draw all common tangents the given circles have.

81. 82. 83.

Write the standard equation of the circle with the given center and radius.

84. Center (–2, -3), radius 7 86. Center (-3, 8), radius 6.2

85. The point (-3,16) is on the circle with center (2,4) 87. The point (2,6) is on the circle with center (-1,2)


Find the measure of the given arc.

88. m DF 89. m JK

90. Find the value of x and y in the diagram below given m FH = 84°, m HS = 80°, m IS = 152°.

91. Assume that the radius of the earth is 3959 miles and that there are no hills or obstructions. If a tourist were standing

atop of the towers of the Eiffel Tower, 1063 feet above the ground, about how far could he see?

92. Earthquakes After an earthquake, you are given seismograph readings from three locations, where the coordinate

unites are miles.

At A(-2, 2.5), the epicenter is 7 miles away.

At B(4, 6), the epicenter is 4 miles away.

At C(3, -2.5), the epicenter is 5 miles away.

a. Graph the three circles in one coordinate plane to

represent the possible epicenter locations determined

by each of the seismograph readings.

b. What are the coordinates of the epicenter?

b.___________

c. People could feel the earthquake up to 9 miles from its epicenter. Could a person at (-6, 7) feel it? Explain.

_____________________________________________________________________________________________

_____________________________________________________________________________________________

_____________________________________________________________________________________________


In Exercises 93-104, find the value(s) of the variable(s).

93. 94. 95.

96. 97. 98.

99. 100. 101.

102. 103. 104.


Find the indicated measure. Round answers to the nearest hundredth.

105. Area of sector ABC 106. Radius of N 107. Circumference of Q

In D shown below, ∠ADC ∠BDC. Find each indicated measure.

108. m ACB

109. m CB

110. Length of ACB

111. Length of CB

112. m ABC

113. Length of BAC

Find the area of the regular polygon. Round answers to the nearest hundredth, if necessary.

114. 115. 116.

Use Euler’s Theorem to find the value of n.

117. Faces: n 118. Faces: 14 119. Faces: 29

Vertices: 12 Vertices: 24 Vertices: n

Edges: 16 Edges: n Edges: 81


The area of R is 295.52 square inches. The area of sector PRQ is 55 square inches. Find each indicated measure.

120. Radius of R

121. Circumference of R

122. m PQ

123. Length of PQ

124. Perimeter of shaded region

125. Perimeter of the unshaded region

Find the area of the shaded region. Round answers to the nearest hundredth, if necessary.

Then find the probability that a randomly chosen point in the figure lies in the shaded region.

126. 127. 128.

129. 130. 131.


Tell whether the solid is a polyhedron. If it is, name the polyhedron, find the number of faces, vertices, and edges.

Explain your reasoning.

132. 133. 134.

135. Find the volume of a cube is 46,656 cm³. What is the surface area of the cube?

136. For the right triangular prism, find:

a. Volume

b. Surface Area

137. The volume of a prism with a square base is 360 cm³, and its height is 10 cm. Find:

a. area of its base.

b. length of a side of the base.

138. Find the surface area of the right square pyramid to the right.

139. Find the exact volume of the oblique cylinder to the right.


140. Find the surface area of the cone below.

141. The figure below is a right cylinder topped by a hemisphere.

a. What is the volume of the figure?

b. What is the surface area of the figure?

142. The volume for a cone is 63π cm³. If its radius is 3 cm, what is its height?

143. Find the surface area and volume of the sphere below.

144. Find the surface area and volume of the cylinder below. (Leave answers in π form.)


Find the volume of the solid. The pyramids are regular and the prisms, cones, and cylinders are right. Round your

answer to two decimal places, if necessary.

145. 146.

147. A pyramid has a square base. Its volume is 507 cm³ and the length of a base edge is 13 cm. Find the height of the

pyramid.

148. A pipe is 8 feet long and 1.5 feet wide. How much water would the pipe be able to hold?

149. Two cones have a scale factor of 3 : 7. The smaller cone has a surface area of 169π square yards. Find the surface

area of the larger cone. Write your answer in terms of π.

150. Two spheres have a scale factor of 2 : 5. The smaller sphere has a volume of about 54π cubic meters. Find the

volume of the larger sphere. Write your answer in terms of π.


151. A hexagon has an area of 90 in² with a side length of 5 in. A similar hexagon has a side length of 4 in. What is the

area of the similar hexagon?

152. A photo measures 5” by 7”. If the shorter dimension of a similar photo is 10”, what is the longer dimension?

153. A swimming pool 10 meters long holds 200,000 liters of water. How much water does a similar pool 15 meters long

hold?

154. If a 10-inch pizza costs $9.50, at the same cost per square inch, what should a 12-inch pizza of the same thickness

with the same ingredients cost?

155. After the introduction of a new soft drink, a taste test is conducted to see how it is being received. Of those who

participated, 48 said they preferred the new soft drink, 112 preferred the old soft drink, and 40 could not tell any

difference. What is the probability that a person in this survey, chosen at random, preferred the new soft drink?

156. A picnic cooler contains 5 sandwiches made with rye bread, 4 sandwiches made with whole wheat bread, 6 made

with oat bread, and 3 made with onion rolls. If only the sandwiches on rye bread and onion rolls have mustard on them,

what is the probability that a sandwich selected randomly from the cooler has mustard on it?


157. A box contains 8 green, 4 yellow, and 8 purple balls. You draw a ball at random. Find the probability of drawing a

green ball.

158. If the probability of an event occurring is , what are the odds in favor of the event?

159. Elaine went to the mall to buy a shirt for a friend. Her choices for the shirt are short sleeved and long sleeved. Both

of the choices come in green, yellow, and blue. Draw a tree diagram that represents her choices.

160. A special deck of cards contains three each of the numbers from 1 to 8 and four each of the numbers 9 and 10. One

card is drawn at random from the deck.

a. What is the probability that the card is a number greater than 7?

b. What is the probability of selecting a card with a number 7?

161. Four people must stand in a row for a group photo. How many different ways can they be lined up for the photo?

162. The Pioneer High track coach has a group of nine runners from which to choose a 4-person relay team. How many

different 4-person teams can be formed from this group of runners.

Find the value of each.

163. 6C4 164. 5! 165. 5P2 166. 11C8

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Geometry Semester Review 2 Semester