geometry mrs. crocker spring 2015 final exam review · 2015-05-15 · geometry mrs. crocker spring...

Name: ___________________________ Mod: ____

Geometry

Mrs. Crocker

Spring 2015

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 5: Relationships within Triangles

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

Mod 3-4: Wednesday 6/3 7:25 – 9:25

Mod 7-8: Tuesday 6/2 9:25 – 11:25

Chapter 5 – Relationships within Triangles

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

diagrams:

A. MIDSEGMENT

B. PERPENDICULAR BISECTORS & CIRCUMCENTER

C. ANGLE BISECTORS & INCENTER

D. MEDIANS & CENTROIDS

E. ALTITUDE & ORTHOCENTER

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

1. Find the value of 𝑥. 2. Find the value of 𝑥 and the 𝑚∠𝑅𝑆𝑇.

3. Find the circumcenter of the triangle. 4. In ∆𝐴𝐶𝐸, G is the centroid and 𝐵𝐸 = 18.

Find 𝐵𝐺 𝑎𝑛𝑑 𝐺𝐸.

5. Two sides of a triangle have lengths 10 and 6. Can the following three lengths be

15. What must be true about the length of the the sides of a triangle? Show work.

third side? 23 𝑚, 17𝑚, 14𝑚

7. Find the possible values for the variable.

Write and solve an inequality.

8. Find the value of the variable.

Write and solve an equation.

Use the figure at the right and the word bank to give the best name to each segment or point. Not

all words will be used.

9. 𝐴𝑄̅̅ ̅̅ : _______________________

10. 𝑅𝐵̅̅ ̅̅ : _______________________

11. 𝐶𝑃̅̅̅̅ : _______________________

12. 𝐴 : ________________________

13. 𝑃 : ________________________

Word Bank:

Vertex

Centroid

Angle Bisector

Perpendicular Bisector

Midpoint

Altitude

Orthocenter

Leg

Median

Midsegment

Chapter 6 - Polygons & Quadrilaterals


diagrams:

F. Angle-Sum Theorem

G. Exterior Angle-Sum Theorem

H. Properties of Parallelograms

I. Rhombus, Rectangle, Square

J. Trapezoid & Kite

K. Midsegment of Trapezoid


14. What is the sum of the angle 15. 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:

16. 72-gon 17. Pentagon

For #18 & 19, find the measure of one exterior angle of the following regular polygons:

18. 36-gon 19. Octagon

For #20 & 21, find the value of x.

20. 21.

List the five properties of parallelograms (notes 6.2):

22. _______________________________________________________________________________________

23. _______________________________________________________________________________________

24. _______________________________________________________________________________________

25. _______________________________________________________________________________________

26. _______________________________________________________________________________________

For #27 & 28, use the properties of parallelograms to find the value of the variable(s).

27. 28.

For #29 & 30, what values of x make each figure the given special parallelogram?

29. rhombus 30. Rectangle

For #31 – 34, decide whether the parallelogram is a rhombus, rectangle, or square. Explain.

31. 32. 33. 34.

For #35 & 36, find x given the midsegment of the trapezoid.

35. 36.

Find the values of the variables of the kite:

37.

Chapter 7 - Similarity


diagrams:

L. Similar Polygons

M. Proving Triangles are Similar

N. Similarity in Right Triangles

O. Proportions in Triangles


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

each of the angles?

39. 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.

40. 41.

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

∆𝐽𝐾𝐿 ~∆𝑄𝑅𝑆

For #43 – 48, use the diagram at the right, ∆𝑵𝑶𝑷~∆𝑾𝑿𝒀. Find each of the following.

43. The scale factor of 44. 𝑁𝑃

∆𝑁𝑂𝑃 𝑡𝑜 ∆𝑊𝑋𝑌

45. 𝑚∠𝑋 46. 𝑁𝑃

𝑊𝑌

47. 𝑚∠𝑌 48. 𝑊𝑋

For #49 – 54, solve for 𝒙 and 𝒚.

49. 50.

51. 52.

53. 54.

For #55 & 56, find the geometric mean for each pair of numbers.

55. 9 𝑎𝑛𝑑 16 56. 5 𝑎𝑛𝑑 80

Chapter 8 - Trigonometry & Right Triangles


diagrams:

P. Converse of the Pythagorean Theorem

Q. 45° − 45° − 90° and 30° − 60° − 90° Triangles

R. Trig Functions

S. Angles of Depression and Elevation


For #57 – 59, the lengths of the sides of a triangle are given. Classify the triangle as acute, right, or

obtuse. Show work.

57. 15, 8, 17 58. 4, 9, 11 59. 5, 6, 7

For #60 & 61, find the value of each variable:

60. y = ________ 61. x = ________

For #62 – 69, find the value of each variable.

62. 63.

64. 65.

66. 67.

68. 69.

For #70 – 73, describe each angle (elevation or depression) as it relates to the situation in the

diagram.

70. ∠1

71. ∠2

72. ∠3

73. ∠4

74. An eagle perched 40 ft up in a tree looks down at a 35° 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.

75. A person is standing 40 ft from a flagpole and can see the top of the pole at a 35° 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:

T. Transformations


76. Define an isometry: _______________________________________________________________________

For #77 & 78, graph the image of each figure under the given translation.

77. (𝑥, 𝑦) → (𝑥, 𝑦 + 5) 78. (𝑥, 𝑦) → (𝑥 + 2, 𝑦 + 4)

For #79 & 80, the dashed-line figure is a translation image of the solid-line figure. Write a rule to

describe each translation.

79. 80.

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

81. A across the y-axis: ____________

82. B across the x-axis: ____________

83. C across y = -1: ____________

84. D across x = -1: ____________

85. E across x = -3: ____________

For #86 – 89, 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.

86. 87.

88. Regular 89. Regular

Pentagon Hexagon

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

diagrams:

U. Area of Parallelograms & Triangles

V. Area of Trapezoids

W. Area of Rhombuses & Kites

X. Area of Regular Polygons

Y. Perimeter & Area of Similar Figures

Z. Arc Length

AA. Area of Sector

BB. Minor Arc vs Major Arc


For #90 – 97, find the area of each figure. Round to the nearest tenth if necessary.

90. 91.

92. 93.

94. 95.

96. 97.

For #98 & 99, find the area of each composite shape.

98. 99.

For #100 & 101, find the measure of each numbered angle:

100. 101.

For #102 & 103, the figures in each pair are similar. What are the ratio of the perimeters and the

ratio of the areas?

102. 103.

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


105. Name a minor arc: __________

106. Name a major arc: __________

107. Name a semicircle: __________

Find the measure of each arc in ⨀𝑹.

108. 𝑚𝑈�̂�: _______ 109. 𝑚𝑈�̂�: _______ 110. 𝑚𝑅�̂�: _______

111. 𝑚𝑈�̂�: _______ 112. 𝑚𝑅𝑈�̂�: _______ 113. 𝑚𝑆𝑇�̂�: _______

For #114 & 115, find the length of the darkened arc. Round answer to the nearest tenth.

114. 115.

For #116 – 119, find the area of the shaded region. Round answers to the nearest tenth.

116. 117.

118. 119.

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

diagrams:

CC. Surface Area of Prisms & Cylinders

DD. Surface Area of Pyramids & Cones

EE. Volume of Prisms & Cylinders

FF. Volume of Pyramids & Cones

GG. Spheres


For #120 – 125, find the surface area of each. Round to the nearest tenth if necessary.

120. 121.

122. 123.

124. 125.

For #126 – 131, find the volume of each. Round to the nearest tenth if necessary.

126. 127.

128. 129.

130. 131.

For #132 & 133, find the surface area and volume of each sphere. Leave answers in terms of 𝝅.

132. 133.

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

134.

geometry mrs. crocker spring 2015 final exam review · 2015-05-15 · geometry mrs. crocker spring...

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