Name: _________________ Mod: ____

Geometry

Mrs. Crocker

Spring 2014

Final Exam Review Use this exam review to complete your “flip book” and to study for your upcoming exam.

You must bring with you to the exam:

1. Pencil, eraser, and calculator

2. Flip Book

You may bring with you to the exam:

1. A handwritten 3x5 notecard with important formulas (both sides may be used)

2. This exam review (at least 50% complete) for extra credit on the exam

Your exam will consist of two parts: Multiple Choice and Free Response covering the following

chapters

Chapter 6: Polygons and Quadrilaterals

Chapter 7: Similarity

Chapter 8: Trigonometry and Right Triangles

Chapter 9: Transformations

Chapter 10: Area

Chapter 11: Surface Area and Volume

Chapter 12: Circles

Mod 5-6: Tuesday 6/3 9:35 - 11:35

Mod 14-15: Monday 6/2 12:25 - 2:25

Chapter 6 - Polygons & Quadrilaterals

In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

A. Angle-Sum Theorem

B. Exterior Angle-Sum Theorem

C. Properties of Parallelograms

D. Rhombus, Rectangle, Square

E. Trapezoid & Kite

F. Midsegment of Trapezoid

Solve the following problems to practice these above concepts. Use a pencil and show work.

1. What is the sum of the angle 2. What is the sum of the angle

measures of a hexagon? measures of an 18-gon?

For #3 & 4, find the measure of one interior angle of the following regular polygons:

3. 72-gon 4. Pentagon

For #5 & 6, find the measure of one exterior angle of the following regular polygons:

5. 36-gon 6. Octagon

For #7 & 8, find the value of x.

7. 8.

List the five properties of parallelograms (notes 6.2):

9. _______________________________________________________________________________________

10. _______________________________________________________________________________________

11. _______________________________________________________________________________________

12. _______________________________________________________________________________________

13. _______________________________________________________________________________________

For #14 & 15, use the properties of parallelograms to find the value of the variable(s).

14. 15.

For #16 & 17, what values of x make each figure the given special parallelogram?

16. rhombus 17. Rectangle

For #20 – 22, decide whether the parallelogram is a rhombus, rectangle, or square. Explain.

18. 19. 20. 21.

For #22 & 23, find x given the midsegment of the trapezoid.

22. 23.

Find the values of the variables of the kite:

24.

Chapter 7 - Similarity

In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

G. Similar Polygons

H. Proving Triangles are Similar

I. Similarity in Right Triangles

J. Proportions in Triangles

Solve the following problems to practice these above concepts. Use a pencil and show work.

25. Two angles are complementary and in the ratio 1 : 4. What are the degree measures of

each of the angles?

26. The measures of the angles of a triangle are in the extended ratio 4 : 6 : 10. What are the

measures of each of the angles?

Determine whether the triangles are similar. If so, write a similarity statement and name the

postulate or theorem you used. If not, explain.

27. 28.

29. Find the value of z. Give the scale factor of the polygons.

For #30 – 35, use the diagram at the right, . Find each of the following.

30. The scale factor of 31.

32. 33.

34. 35.

For #36 – 39, solve for and .

36. 37.

38. 39.

40. 41.

For #42 & 43, find the geometric mean for each pair of numbers.

42. 43.

Chapter 8 - Trigonometry & Right Triangles

In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

K. Converse of the Pythagorean Theorem

L. and Triangles

M. Trig Functions

N. Angles of Depression and Elevation

Solve the following problems to practice these above concepts. Use a pencil and show work.

For #44 – 46, the lengths of the sides of a triangle are given. Classify the triangle as acute, right, or

obtuse. Show work.

44. 15, 8, 17 45. 4, 9, 11 46. 5, 6, 7

For #47 & 48, find the value of each variable:

47. y = ________ 48. x = ________

For #49 – 56, find the value of each variable.

49. 50.

51. 52.

53. 54.

55. 56.

For #57 – 60, describe each angle (elevation or depression) as it relates to the situation in the

diagram.

27.

28.

29.

60.

61. An eagle perched 40 ft up in a tree looks down at a angle and spots a vole. How far is

the vole from the eagle to the nearest tenth of a foot? Draw and label a diagram.

62. A person is standing 40 ft from a flagpole and can see the top of the pole at a angle of

elevation. The person’s eye level is 4 ft from the ground. What is the height of the flagpole to the

nearest foot? Draw and label a diagram.

Chapter 9 - Transformations In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

O. Transformations

Solve the following problems to practice these above concepts. Use a pencil and show work.

63. Define an isometry: _______________________________________________________________________

For #64 & 65, graph the image of each figure under the given translation.

64. ( ) ( ) 65. ( ) ( )

For $66 & 67, the dashed-line figure is a translation image of the solid-line figure. Write a rule to

describe each translation.

66. 67.

Each point is reflected across the line indicated. Find the coordinates of each image.

68. A across the y-axis: ____________

69. B across the x-axis: ____________

70. C across y = -1: ____________

71. D across x = -1: ____________

72. E across x = -3: ____________

For #73 & 74, given points M(-1, 3), N(2, -2), and O(3, 1), graph and its reflection image

across the line and apply a dilation with center (0,0) and scale factor 2.

73. x = 2 74. Dilate with scale factor of 2

For #75 – 78, tell what type(s) of symmetry each figure has. It if has line symmetry, sketch the

line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation.

75. 76. 77. Regular 78. Regular

Pentagon Hexagon

The dashed-line figure is a dilation image of the solid-line figure. The labeled point is the center.

Tell whether the dilation is an enlargement or a reuction. Then find the scale factor.

79. 80.

Chapter 10 - Area In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

P. Area of Parallelograms & Triangles

Q. Area of Trapezoids

R. Area of Rhombuses & Kites

S. Area of Regular Polygons

T. Perimeter & Area of Similar Figures

Solve the following problems to practice these above concepts. Use a pencil and show work.

For #81 – 88, find the area of each figure. Round to the nearest tenth if necessary.

81. 82.

83. 84.

85. 86.

87. 88.

For #89 & 90, find the area of each composite shape.

89. 90.

For #91 & 92, find the measure of each numbered angle:

91. 92.

For #93 & 94, the figures in each pair are similar. What are the ratio of the perimeters and the ratio

of the areas?

93. 94.

95. The areas of two similar triangles are 25 m 2 and 49 m2. Find their scale factor.

Chapter 11 - Surface Area & Volume In your flip books complete the following topics. Write necessary formulas, information, and draw

diagrams:

U. Surface Area of Prisms & Cylinders

V. Surface Area of Pyramids & Cones

W. Volume of Prisms & Cylinders

X. Volume of Pyramids & Cones

Y. Spheres

Solve the following problems to practice these above concepts. Use a pencil and show work.

For #96 – 101, find the surface area of each. Round to the nearest tenth if necessary.

96. 97.

98. 99.

100. 101.

For #102 – 107, find the volume of each. Round to the nearest tenth if necessary.

102. 103.

104. 105.

106. 107.

For #108 & 109, find the surface area and volume of each sphere. Leave answers in terms of .

108. 109.

Find the surface area and volume of the composite shape. Leave answers in terms fo .

110.

Chapter 12 - Circles (also 10.6 & 10.7) In your flip books complete the following topics. Write necessary formulas, information, and

draw diagrams:

Z. Arc Length

AA. Area of Sector

BB. Tangent Lines

CC. Chords & Arcs

DD. Inscribed Angles

Solve the following problems to practice these above concepts. Use a pencil and show work.

111. Name a minor arc: __________

112. Name a major arc: __________

113. Name a semicircle: __________

Find the measure of each arc in .

114. ̂: _______ 115. ̂: _______ 116. ̂: _______

117. ̂: _______ 118. ̂: _______ 119. ̂: _______

For #120 & 121, find the length of the darkened arc. Round answer to the nearest tenth.

120. 121.

For #122 – 125, find the area of the shaded region. Round answers to the nearest tenth.

122. 123.

124. 125.

For #126 – 133, all lines that appear tangent are tangent. Find the value of the variable(s).

126. 127.

128. 129.

130. 131.

132. 133.

Determine whether a tangent line is shown.

132.