geometry mrs. crocker spring 2015 final exam review · 2015-05-15 · geometry mrs. crocker spring...
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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
In your flip books complete the following topics. Write necessary formulas, information, and draw
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
Solve the following problems to practice these above concepts. Use a pencil and show work.
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
In your flip books complete the following topics. Write necessary formulas, information, and draw
diagrams:
L. Similar Polygons
M. Proving Triangles are Similar
N. Similarity in Right Triangles
O. Proportions in Triangles
Solve the following problems to practice these above concepts. Use a pencil and show work.
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
In your flip books complete the following topics. Write necessary formulas, information, and draw
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
Solve the following problems to practice these above concepts. Use a pencil and show work.
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
Solve the following problems to practice these above concepts. Use a pencil and show work.
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
Solve the following problems to practice these above concepts. Use a pencil and show work.
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.
Solve the following problems to practice these above concepts. Use a pencil and show work.
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
Solve the following problems to practice these above concepts. Use a pencil and show work.
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.