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NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Geometry Final Exam Review 2014-2015
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1-4, refer to the figure.
1. Name a median.
A 𝑅𝑊
B ⃡𝑆𝑉
C 𝑄𝑇
D 𝑅𝑈
̅̅̅̅
H 𝑄𝑇
J 𝑅𝑈
⃡
B 𝑆𝑉
̅̅̅̅
C 𝑄𝑇
D 𝑅𝑈
G ̅̅̅̅
𝑅𝑃
H ̅̅̅̅
𝑄𝑇
J 𝑅𝑈
2. Name an angle bisector.
̅̅̅̅̅
F 𝑅𝑊
⃡
G 𝑆𝑉
3. Name a perpendicular bisector.
̅̅̅̅̅
A 𝑅𝑊
4. Name an altitude.
F ̅̅̅̅̅
𝑅𝑊
For Questions 5-7, refer to the figure to determine which is a true statement for the given information.
5. ̅̅̅̅
𝐹𝐺 is an altitude.
A ∠ DGF is a right angle.
B DF = EF
C DG = GE
D ∠ DFG ≅ ∠ EFG
6. ̅̅̅̅
𝐹𝐺 is a median.
F ∠ DGF is a right angle.
G DF = EF
H DG = GE
J ∠ DFG ≅ ∠ EFG
̅̅̅̅ is an angle bisector.
7. 𝐹𝐺
A ∠ DGF is a right angle.
B DF = EF
C DG = GE
D ∠ DFG ≅ ∠ EFG
8. Name the longest side of △ABC.
F ̅̅̅̅
𝐴𝐵
G ̅̅̅̅
𝐵𝐶
H ̅̅̅̅
𝐴𝐶
J cannot tell
9. Name the angle with the greatest measure in △GHI.
A ∠G
B ∠H
C ∠I
D cannot tell
10. Carrie, Maria, and Nayla are friends that
live close to one another. Which two friends
have the shortest distance between them?
A Maria and Nayla
B Carrie and Maria
C Carrie and Nayla
D All three live equal distances from each other.
11. Find the possible values for m∠ 1.
F m∠ 1 = 124
G 0 < m∠ 1 < 5
H 90 > m∠ 1 > 56
J 180 > m∠ 1 > 56
12. Which of the following sets of numbers can be the lengths of the sides of a triangle?
A 12, 9, 2
B 11, 12, 23
C 2, 3, 4
D √3,√5,√18
13. If point E is the centroid of △ABC, BD = 12, EF = 7, and AG = 15, find ED.
14. List the angles of △GHI in order from largest to smallest measure.
15. List the sides of △PQR in order from longest to shortest.
16. Find x in △PQR.
A 13
B 15
C 16
D √60
G8
H √32
J √514
17. Find x in △STU.
F2
18. Which set of measures could represent the lengths of the sides of a right triangle?
A 2, 3, 4
B 7, 11, 14
C 8, 10, 12
D 9, 12, 15
19. Find x in △DEF.
F6
G 6√2
H 6√3
J 12
B 15√3
C 15
D 30
19. Find y in △XYZ.
A 7.5√3
20. The length of the sides of a square is 10 meters. Find the length of the diagonals of the square.
F 10 m
G 10√2 m
H 10√3 m
21. Find x in △HJK.
A 5 √2
22. Find x in △ABC.
F 25
B 5 √3
C 10
D 15
G 25√2
H 𝟐𝟓√3
J 100
C 18.4
D 47.1
23. Find x to the nearest tenth.
A 7.3
B 17.3
J 20 m
24. Find the measure of the angle of elevation of the Sun when a pole 25 feet tall casts a shadow 42 feet long.
F 30.8°
G 36.5°
H 53.5°
J 59.2°
25. Which is the angle of depression in the figure at the right?
A ∠ AOT
B ∠ AOB
C ∠ TOB
D ∠ BTO
Solve for each missing variable.
26.
27.
x = _________
28.
x = _________
29.
x = _________
x = _________
30.
x = _________
y = _________
31. A 38-foot tree casts a 16-foot shadow. Find the measure of the angle of elevation of the sun to the nearest degree.
32. A boat is 2000 meters from a cliff. If the angle of depression from the top of the cliff to the boat is 10°, how tall is the
cliff? Round your answer to the nearest tenth.
32. A plane flying at an altitude of 10,000 feet begins descending when the end of the runway is 60,000 feet from a point
on the ground directly below the plane. Find the measure of the angle of descent (depression) to the nearest degree.
33. Given B(–4, –6), under which reflection is B′(4, –6)?
A reflected in the x-axis
B reflected in the y-axis
C reflected in the line y = –2
D reflected in the line y = x
34. Which transformation turns every point of the preimage through a specified angle and direction about a fixed point?
F reflection
G rotation
H translation
J dilation
35. What kind of transformation is represented in the figure at the right?
A translation
B rotation
C reflection
D dilation
̅̅̅̅ with endpoints C(5, –7) and D(–3, 9) is rotated 270° about the origin. What is the coordinate of
36. The line segment 𝐶𝐷
D'?
A D'(–3, –9)
B D'(3, –9)
C D'(9, –3)
D D'(9, 3)
H A'(6, 1)
J A'(–1, 6)
37. Find the reflection of the point A(6, –1) in the x-axis.
F A'(6, –1)
G A'(–6, 1)
38. Graph △TUV with vertices T(3, 3), U(6, –1), and V(–2, 1). Then graph the image of △TUV reflected in the line y = 2.
y
10
9
8
7
6
5
4
3
2
1
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
39. Find the sum of the measures of the interior angles of a convex 45-gon.
A 8100
B 7740
C 360
D 172
G 66
H 102
J 138
40. Find the value of x.
F 30
41. Find the sum of the measures of the exterior angles of a convex 39-gon.
A 39
B 90
C 180
D 360
42. Which of the following is a property of a parallelogram?
F Each pair of opposite sides is congruent.
G Only one pair of opposite angles is congruent.
H Each pair of opposite angles is supplementary.
J There are four right angles.
1
2
3
4
5
6
7
8
9
10
x
43. For parallelogram ABCD, find m∠1.
A 60
B 54
C 36
D 18
44. ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find the value of x.
F5
G 17
H 27
J 47
45. Find the values of x and y so that this quadrilateral is a parallelogram.
A x = 13, y = 24
B x = 13, y = 6
C x = 7, y = 24
D x = 7, y = 6
46. Find the value of x so that this quadrilateral is a parallelogram.
F 12
G 24
H 36
J 132
47. Parallelogram ABCD has vertices A(8, 2), B(6, –4), and C(–5, –4). Find the coordinates of D.
A D(–5, 2)
B D(–3, 2)
C D(–2, 2)
D D(–4, 8)
48. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find the value of x.
F5
G6
H 11
J 26
49. Which of the following is true for all rectangles?
A The diagonals are perpendicular.
B The diagonals bisect the angles.
C The consecutive sides are congruent.
D The consecutive sides are perpendicular
50. ABCD is a rectangle with B(–4, 6), C(–4, 2), and D(10, 2). Find the coordinates of A.
F A(6, 4)
G A(10, 4)
H A(2, 6)
J A(10, 6)
C 68
D 90
51. For rhombus GHJK, find m∠1.
A 22
B 44
52. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x – 10, find AC.
F 11
G 28
H 56
J 90
53. ABCD is an isosceles trapezoid with A(10, -1), B(8, 3), and C(-1, 3). Find the coordinates of D.
A D(–3, –1)
B D(–10, –11)
C D(–1, 8)
D D(–3, 3)
54. For isosceles trapezoid MNOP, find m∠MNP.
F 44
G 64
H 80
J 116
55. The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length of the
other base.
A 35 in.
B 19 in.
C 17.5 in.
D 13 in
56. Judith built a fence to surround her property. On a coordinate plane, the four corners of the fence are located at
(–16, 1), (–6, 5), (4, 1), and (–6, –3). Which of the following most accurately describes the shape of Judith’s fence?
F square
G rectangle
H rhombus
J trapezoid
57. For kite PQRS, find m∠S.
A 248
B 68
Solve.
58.
C 112
D 124
59.
x = _______
60.
x = _______
x = _______
Solve. Each figure is a parallelogram.
61.
x = ______ y = ______ z = ______
62.
x = ______ y = ______ z = ______
63.
x = ______ y = ______ z = ______
64. Determine whether ABCD is a parallelogram. Justify your answer.
65. The length of the median of trapezoid EFGH is 13 feet. If the bases have lengths 2x + 4 and 10x – 50, find x.
66. ABCD is a kite, If RC = 10, and BD = 48, find CD.
67. Of the 300 television sets sold at an electronics store last month, 90 were flat-screen TVs. What is the ratio of flatscreen TVs to other TVs sold last month?
68. Determine whether △ABC ∼ △DEF. Justify your answer.
69. When a 5-foot vertical pole casts a 3-foot 4-inch shadow, an oak tree casts a 20-foot shadow. Find the height of the
tree.
2
70. Quadrilateral ABCD ∼ quadrilateral WXYZ, AB = 15, BC = 27, BC = 27, and the scale factor of WXYZ to ABCD is .
3
Find XY.
1
71. The blueprint for a swimming pool is 8 inches by 2 2 inches. The actual pool is 136 feet long. Find the width of the
pool.
72. Find CD.
73. If quadrilateral ABCD ∼ quadrilateral PQRS, find BC.
74. △ABC ∼ △XYZ, AB = 12, AC = 16, BC = 20, and XZ = 24. Find the perimeter of △XYZ.
For Questions 75 and 76, use the figure.
75. Identify the similar triangles.
76. Find the value of x.
77. The ratio of the measures of the three sides of a triangle is 3:4:6. If the perimeter is 91, find the length of the longest
side.
78. If △RST ∼ △UVW, find m∠W.
79. Find the value of y so that 𝑀𝑁 || 𝐵𝐶.
80. Find the value of x.
For Questions 81-83, use the figure to the right.
81. Name a radius.
A ̅̅̅̅
𝑋𝐵
B ̅̅̅̅
𝐴𝐵
C ̅̅̅̅
𝐵𝐶
D ⃡𝐴𝐶
̅̅̅̅̅
G 𝑋𝐶
̅̅̅̅
H 𝐵𝐶
⃡
D 𝐴𝐶
B ̅̅̅̅̅
𝐵𝐶
C ⃡𝐴𝐶
D ⃡𝐵𝐷
82. Name a chord.
F ̅̅̅̅
𝑋𝐵
83. Name a tangent.
A ̅̅̅̅
𝐴𝐵
84. The wheels on Elliot’s truck each have a circumference of 22 inches. Determine the radius of each wheel to the
nearest length.
F 2.5 in.
G 3.5 in.
H 5 in.
J 7 in.
̂ = 72. Find m∠BCD.
85. In ⨀C, m𝐴𝐵
A 72
B 108
C 144
D 180
̂ in ⨀R to the nearest hundredth.
86. Find the length of 𝑃𝑄
F 9.42 m
G 4.71 m
H 3.14 m
J 1.57 m
87. Find YB if the diameter of ⨀A is 10 inches, the diameter of ⨀B is 8 inches, and AX = 3 inches.
88. Find the radius and diameter of a flying disc with a circumference of 11π inches.
̂.
89. In ⨀K, m∠HKG = x + 10 and m∠IKJ = 3x – 22. Find m 𝐹𝐽
90. The diameter of ⨀C is 18 units long. Find the length of an arc that has a measure of 100. Round to the nearest
hundredth.