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Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry Final Exam Review 2015

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. What is the value of x if ABC is equilateral?

a. −8 c.1

2

b. −1

8d. 2

Use the figure below.

____ 2. What is m∠2?

a. 50 c. 110

b. 70 d. 120

____ 3. What is m∠4?

a. 10 c. 100

b. 60 d. 120

____ 4. What are the congruent triangles in the diagram?

a. ABC ≅ EBD c. AEB ≅ CBD

b. ABE ≅ CBD d. ABE ≅ CDB

Name: ________________________ ID: A

2

____ 5. If CJW ≅ AGS, m∠A = 50, m∠J = 45, and m∠S = 16x + 5, what is x?

a. 17.5 c. 6

b. 11.875 d. 5

____ 6. A triangular-shaped roof of a house has congruent legs. What is the measure of each of the two base angles?

a. 25 c. 100

b. 50 d. 120

____ 7. What is the length of the sides of this equilateral triangle?

a. 42 c. 15

b. 30 d. 12

____ 8. How would ABC with vertices A(4, 1), B(2, −1), and C(−2, −1) be classified based on its sides?

a. equilateral c. scalene

b. isosceles d. right

____ 9. If DJL ≅ EGS, which segment in EGS corresponds to DL ?

a. EG c. GS

b. ES d. GE

____ 10. Which triangles are congruent in the figure?

a. KLJ ≅ MNL c. JKL ≅ LMN

b. JLK ≅ NLM d. JKL ≅ MNL

Name: ________________________ ID: A

3

____ 11. If ABC is isosceles and AE ≅ FC, which theorem or postulate can be used to prove AEB ≅ CFB?

a. SSS c. ASA

b. SAS d. AAS

____ 12. Find the sum of the measures of the interior angles of a convex 30-gon.

a. 5400 c. 360

b. 5040 d. 168

____ 13. Find the sum of the measures of the exterior angles of a convex 21-gon.

a. 21 c. 360

b. 180 d. 3420

____ 14. If the measure of each interior angle of a regular polygon is 108, find the measure of each exterior angle.

a. 18 c. 90

b. 72 d. 108

____ 15. For parallelogram ABCD, find x.

a. 4 c. 16

b. 10.25 d. 21.5

____ 16. Which of the following is a property of a parallelogram?

a. The diagonals are congruent. c. The diagonals are perpendicular.

b. The diagonals bisect the angles. d. The diagonals bisect each other.

____ 17. Find x and y so that ABCD will be a parallelogram.

a. x = 6, y = 42 c. x = 20, y = 42

b. x = 6, y = 22 d. x = 20, y = 22

____ 18. Find x so that this quadrilateral is a parallelogram.

a. 44 c. 90

b. 46 d. 134

Name: ________________________ ID: A

4

____ 19. Parallelogram ABCD has vertices A(0, 0), B(2, 4), and C(10, 4). Find the possible coordinates of D.

a. (8, 0) c. (0, 4)

b. (10, 0) d. (10, 8)

____ 20. Which of the following is a property of all rectangles?

a. four congruent sides c. diagonals are perpendicular

b. diagonals bisect the angles d. four right angles

____ 21. ABCD is a rectangle with diagonals AC and BD. If AC = 2x + 10 and BD = 56, find x.

a. 23 c. 78

b. 33 d. 122

____ 22. ABCD is a rectangle with B(−5, 0), C(7, 0) and D(7, 3). Find the coordinates of A.

a. (−5, 7) c. (−5, 3)

b. (3, 5) d. (7, −3)

____ 23. For rhombus ABCD, find m∠1.

a. 45 c. 90

b. 60 d. 120

____ 24. Find m∠PRS in square PQRS.

a. 30 c. 60

b. 45 d. 90

____ 25. Choose a pair of base angles of trapezoid ABCD.

a. ∠A, ∠C c. ∠A, ∠D

b. ∠B, ∠D d. ∠D, ∠C

____ 26. In trapezoid DEFG, find m∠D.

a. 44 c. 108

b. 72 d. 136

Name: ________________________ ID: A

5

____ 27. The hood of Olivia’s car is the shape of a trapezoid. The base bordering the windshield measures 30 inches

and the base at the front of the car measures 24 inches. What is the width of the median of the hood?

a. 25 in. c. 28 in.

b. 27 in. d. 29 in.

____ 28. The length of one base of a trapezoid is 44, the median is 36, and the other base is 2x + 10. Find x.

a. 9 c. 21

b. 17 d. 40

____ 29. Given trapezoid ABCD with median EF, which of the following is true?

a. EF =1

2AD c. AB = EF

b. AE = FD d. EF =BC + AD

2

____ 30. ABCD is a rectangle with A(0, 0), B(b, 0), and D(0, a). Find the coordinates of C.

a. C(a, b) c. C(2b, a)

b. C(b, a) d. C(a + b, a)

____ 31. To prove that the diagonals of a square bisect each other, you would position and label a square in the

coordinate plane and then find which of the following?

a. measures of the angles c. lengths of the diagonals

b. midpoints of the diagonals d. slopes of the diagonals

____ 32. Find the sum of the measures of the interior angles of a convex 45-gon.

a. 8100 c. 360

b. 7740 d. 172

____ 33. Find x.

a. 30 c. 102

b. 66 d. 138

____ 34. Find the sum of the measures of the exterior angles of a convex 39-gon.

a. 39 c. 180

b. 90 d. 360

____ 35. Which of the following is a property of a parallelogram?

a. Each pair of opposite sides is congruent.

b. Only one pair of opposite angles is congruent.

c. Each pair of opposite angles is supplementary.

d. There are four right angles.

Name: ________________________ ID: A

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____ 36. For parallelogram ABCD, find m∠1.

a. 60 c. 36

b. 54 d. 18

____ 37. ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find x.

a. 5 c. 27

b. 17 d. 47

____ 38. Find x and y so that this quadrilateral is a parallelogram.

a. x = 13, y = 24 c. x = 7, y = 24

b. x = 13, y = 6 d. x = 7, y = 6

____ 39. Find x so that this quadrilateral is a parallelogram.

a. 12 c. 36

b. 24 d. 132

____ 40. Parallelogram ABCD has vertices A(8, 2), B(6, −4), and C(−5, −4). Find the coordinates of D.

a. D(−5, 2) c. D(−2, 2)

b. D(−3, 2) d. D(−4, 8)

____ 41. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find x.

a. 5 c. 11

b. 6 d. 26

____ 42. Which of the following is true for all rectangles?

a. The diagonals are perpendicular. c. The consecutive sides are congruent.

b. The diagonals bisect the angles. d. The consecutive sides are perpendicular.

____ 43. ABCD is a rectangle with B(−4, 6), C(−4, 2), and D(10, 2). Find the coordinates of A.

a. A(6, 4) c. A(2, 6)

b. A(10, 4) d. A(10, 6)

Name: ________________________ ID: A

7

____ 44. For rhombus GHJK, find m∠1.

a. 22 c. 68

b. 44 d. 90

____ 45. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x − 10, find AC.

a. 11 c. 56

b. 28 d. 90

____ 46. ABCD is an isosceles trapezoid with A(10, −1), B(8, 3), and C(−1, 3). Find the coordinates of D.

a. (−3, −1) c. (−1, 8)

b. (−10, −11) d. (−3, 3)

____ 47. For isosceles trapezoid MNOP, find m∠MNP.

a. 44 c. 80

b. 64 d. 116

____ 48. 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. c. 17.5 in.

b. 19 in. d. 13 in.

____ 49. 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?

a. square c. rhombus

b. rectangle d. trapezoid

____ 50. What type of quadrilateral has vertices at (0, 0), (a, b), (c, b), and (c + a, 0)?

a. parallelogram c. rhombus

b. rectangle d. trapezoid

____ 51. To prove that the diagonals of a rhombus are perpendicular to each other, you would position and label a

rhombus on a coordinate plane and then find which of the following?

a. measures of the angles c. lengths of the diagonals

b. slopes of the diagonals d. midpoints of the diagonals

____ 52. There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples to plums?

a. 3:5 c. 5:3

b. 3:8 d. 8:3

____ 53. The scale drawing of a porch is 8 inches wide by 12 inches long. If the actual porch is 12 feet wide, what is

the length of the porch?

a. 8 ft c. 16 ft

b. 10 ft d. 18 ft

Name: ________________________ ID: A

8

____ 54. Solve 5

6=

4

x.

a. 4.6 c. 5

b. 4.8 d. 7

____ 55. A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample

was representative, find the number of bulbs expected to be defective in a case of 450.

a. 24 c. 36

b. 30 d. 45

____ 56. Find the triangle similar to ABC below

a. c.

b. d.

____ 57. Find x if ABC ~ JKL.

a. 10 c. 25

b. 14 d. 29

____ 58. Quadrilateral ABCD ∼ quadrilateral PQRS. If AB = 10, BC = 6, PS = 12, and QR = 4, find the scale factor of

ABCD to PQRS.

a.1

2c.

5

3

b.3

2d.

5

6

____ 59. Quadrilateral ABCD ∼ quadrilateral EFGH. Find x.

a. 15 c. 25

b. 20 d. 30

Name: ________________________ ID: A

9

____ 60. Which theorem or postulate can be used to prove that these two triangles are similar?

a. AA c. SSA

b. SAS d. SSS

____ 61. Find MN.

a. 51

3c. 7

b. 63

4d. 12

____ 62. A 5-foot tall student cast a 4-foot shadow. If the tree next to her cast a 44-foot shadow, what is the height of

the tree?

a. 351

5ft c. 51

1

2ft

b. 45 ft d. 55 ft

____ 63. In ABC, DE Ä AC. If AD = 12, BD = 3, and CE = 10, find BE.

a. 1 c. 2

b. 11

2d. 2

1

2

____ 64. In ABC AC Ä MN. What is x?

a. 8 c. 25

b. 10 d. 29

Name: ________________________ ID: A

10

____ 65. Find x.

a. 14 c. 16

b. 15 d. 18

____ 66. FGH ∼ PQR, FG = 6, PQ = 10, and the perimeter of PQR is 35. What is the perimeter of FGH?

a. 21 c. 31

b. 27 d. 581

3

____ 67. LMN ~ XYZ with altitudes KL and WX. Find KL.

a. 6 c. 9

b. 7 d. 19

____ 68. Find x.

a. 5 c. 61

2

b. 6 d. 71

2

____ 69. Find x.

a. 16 c. 20

b. 18 d. 21

____ 70. Nathan is building a model of his father’s sailboat with a scale factor of 1

32. The actual sail is in the shape of

a right triangle with a base of 8 meters and a hypotenuse of 13 meters. What will be the approximate

perimeter of the sail on the model boat?

a. 32 cm c. 65.62 cm

b. 48.81 cm d. 97.65 cm

Name: ________________________ ID: A

11

____ 71. Of the 240 students eating lunch, 96 purchased their lunch and the rest brought a bag lunch. What is the ratio

of students purchasing lunch to students bringing a bag lunch?

a. 2:3 c. 3:2

b. 2:5 d. 5:2

____ 72. In a rectangle, the ratio of the width to the length is 4:5. If the rectangle is 40 centimeters long, find its width.

a. 32 cm c. 44 cm

b. 36 cm d. 50 cm

____ 73. A postage stamp 25 millimeters wide and 40 millimeter tall is enlarged to make a poster. The poster is 4 feet

wide. Find the height of the poster.

a. 2.5 ft c. 5.8 ft

b. 5.25 ft d. 6.4 ft

____ 74. Find the polygon that is similar to ABCD.

a. c.

b. d.

____ 75. If PQR ∼ STU, find x.

a. 4.4 c. 24.6

b. 7 d. 35

____ 76. If ABCD ∼ EFGH, find x.

a. 18.75 c. 22.75

b. 20 d. 28

____ 77. ABC ~ LMN, AB = 18, BC = 12, LN = 9, and LM = 6. What is the scale factor of ABC to LMN?

a.9

2c.

3

1

b.3

2d.

2

1

Name: ________________________ ID: A

12

____ 78. Name the theorem or postulate that can be used to prove that these triangles are similar.

a. AA Similarity c. SAS Similarity

b. SSS Similarity d. SSA Similarity

Refer to the figure below.

____ 79. Identify the true statement.

a. PQR ∼ RST c. PQR ∼ TSR

b. PQR ∼ STR d. PQR ∼ TRS

____ 80. Find x.

a. 21

2c. 3

1

2

b. 3 d. 4

____ 81. A 24-foot flagpole cast a 20-foot shadow. The building next to it cast an 85-foot shadow. Find the height of

the building.

a. 705

6ft c. 96

1

6ft

b. 89 ft d. 102 ft

____ 82. Find QT.

a. 15 c. 19

b. 17 d. 21

Name: ________________________ ID: A

13

____ 83. Find x so that ST Ä PR.

a. 4 c. 6

b. 41

2d. 6

1

2

____ 84. Find y.

a.4

3c.

7

3

b. 2 d. 3

____ 85. If KLM ∼ XYZ, find the perimeter of XYZ.

a. 40 c. 45

b. 42 d. 48

____ 86. ABC ∼ JKL with altitudes BX and KY. Find BX.

a. 19.2 c. 24.6

b. 21 d. 28

____ 87. Find x.

a. 4 c. 6

b. 5 d. 8

Name: ________________________ ID: A

14

____ 88. Find y.

a. 21

4c. 3

1

2

b. 23

4d. 4

1

2

Use X.

____ 89. Name a radius.

a. XB c. BC

b. AB d. AC→←

____ 90. Name a chord.

a. XB c. BC

b. XC d. AC→←

____ 91. Name a tangent.

a. AB c. AC→←

b. BC d. BD→←

____ 92. The wheels on Elliot’s truck each have a circumference of 22 inches. Determine the radius of each wheel.

a. 2.5 in. c. 5 in.

b. 3.5 in. d. 7 in.

____ 93. In C, mAB = 72. Find m∠BCD.

a. 72 c. 144

b. 108 d. 180

Name: ________________________ ID: A

15

____ 94. Find the length of PQ in R to the nearest hundredth.

a. 9.42 m c. 3.14 m

b. 4.71 m d. 1.57 m

____ 95. In O, AB = 12 centimeters, OE = 4 centimeters, and OF = 4 centimeters. Find CF.

a. 6 cm c. 12 cm

b. 8 cm d. 24 cm

____ 96. Find the radius of a circle if a 48-meter chord is 7 meters from the center.

a. 14 m c. 25 m

b. 24 m d. 41 m

____ 97. Find m∠ABC.

a. 50 c. 90

b. 70 d. 140

____ 98. If m∠X = 126, find m∠Z.

a. 54 c. 90

b. 63 d. 126

Name: ________________________ ID: A

16

____ 99. If MN, NO, and MO are tangent to P, find x.

a. 2 m c. 6 m

b. 5 m d. 8 m

____ 100. Find x.

a. 122 c. 68

b. 95 d. 61

____ 101. Find y.

a. 16 c. 80

b. 56 d. 112

____ 102. Find z.

a. 38 c. 58

b. 56 d. 76

____ 103. Find x.

a. 132 c. 66

b. 68 d. 34

Name: ________________________ ID: A

17

____ 104. Find y.

a. 18 c. 6

b. 12 d. 4.5

____ 105. Find z.

a. 11.25 c. 7.5

b. 10 d. 4

____ 106. Find the radius of the circle whose equation is (x + 3)2 + (y − 7)2 = 289.

a. 7 c. 34

b. 17 d. 289

____ 107. Find the equation of a circle with center (0 , 0) and radius 4.

a. x2 + y2 = 4. c. (x − 4)2 + (y − 4)2 = 16

b. x2 + y2 = 16. d. 4x + 4y = 16

____ 108. Identify the graph of (x − 3)2 + (y + 2)2 = 4.

a. c.

b. d.

Name: ________________________ ID: A

18

Use O.

____ 109. Name a diameter.

a. FG c. AB→←

b. AB d. CE→←

____ 110. Name a chord.

a. FO c. AB→←

b. AB d. CE→←

____ 111. Name a secant.

a. FO c. AB→←

b. AB d. CE→←

____ 112. The diameter of a circular swimming pool is 15 feet. Find the circumference to the nearest hundredth.

a. 47.12 ft c. 75.96 ft

b. 63.81 ft d. 94.24 ft

____ 113. In A, m∠BAD = 110. Find mDE.

a. 35 c. 70

b. 55 d. 110

____ 114. Find x.

a. 122 c. 58

b. 61 d. 29

____ 115. EFGH is a quadrilateral inscribed in P with m∠E = 72 and m∠F = 49. Find m∠H.

a. 131 c. 90

b. 108 d. 57

Name: ________________________ ID: A

19

____ 116. Find x.

a. 78 c. 102

b. 90 d. 156

____ 117. Find y.

a. 66 c. 45

b. 57 d. 21

____ 118. Find the center of the circle whose equation is (x + 11)2 + (y − 7)2 = 121.

a. (−11, 7) c. (121, 49)

b. (11, −7) d. 11

____ 119. Find the equation of a circle whose center is at (2, 3) and radius is 6.

a. (x + 2)2 + (y + 3)2 = 6. c. (x + 2)2 + (y + 3)2 = 36

b. (x − 2)2 + (y − 3)2 = 6. d. (x − 2)2 + (y − 3)2 = 36

____ 120. Find the equation of P.

a. x2 + (y − 3)2 = 4. c. (x − 3)2 + y2 = 2

b. x2 + (y − 3)2 = 2. d. (x − 3)2 + y2 = 4

ID: A

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57. ANS: D PTS: 1 NAT: NA1| NA2| NA3


59. ANS: C PTS: 1 NAT: NA1| NA2| NA3

60. ANS: A PTS: 1 NAT: NA1| NA3| NA7

























ID: A

3





































ID: A Geometry Final Exam Review 2015 [Answer Strip]

_____ 1.D

_____ 2.A

_____ 3.C

_____ 4.B

_____ 5.D

_____ 6.B

_____ 7.C

_____ 8.C

_____ 9.B

_____ 10.D

_____ 11.B

_____ 12.B

_____ 13.C

_____ 14.B

_____ 15.C

_____ 16.D

_____ 17.A

_____ 18.B

_____ 19.A

_____ 20.D

_____ 21.A

_____ 22.C

_____ 23.C

_____ 24.B

_____ 25.D

_____ 26.A

_____ 27.B

_____ 28.A

_____ 29.D

_____ 30.B

_____ 31.B

_____ 32.B

_____ 33.B

_____ 34.D

_____ 35.A


_____ 36.C

_____ 37.A

_____ 38.A

_____ 39.C

_____ 40.B

_____ 41.A

_____ 42.D

_____ 43.D

_____ 44.C

_____ 45.C

_____ 46.A

_____ 47.B

_____ 48.D

_____ 49.C

_____ 50.D

_____ 51.B

_____ 52.A

_____ 53.D

_____ 54.B

_____ 55.B

_____ 56.B

_____ 57.D

_____ 58.B

_____ 59.C

_____ 60.A

_____ 61.B

_____ 62.D

_____ 63.D

_____ 64.A

_____ 65.B

_____ 66.A

_____ 67.B

_____ 68.D

_____ 69.C

_____ 70.D


_____ 71.A

_____ 72.A

_____ 73.D

_____ 74.C

_____ 75.B

_____ 76.C

_____ 77.C

_____ 78.A

_____ 79.C

_____ 80.B

_____ 81.D

_____ 82.D

_____ 83.B

_____ 84.B

_____ 85.C

_____ 86.A

_____ 87.A

_____ 88.A

_____ 89.A

_____ 90.C

_____ 91.D

_____ 92.B

_____ 93.B

_____ 94.C

_____ 95.A

_____ 96.C

_____ 97.B

_____ 98.A


_____ 99.D

_____100.B

_____101.C

_____102.B

_____103.D

_____104.D

_____105.B

_____106.B

_____107.B

_____108.D

_____109.A

_____110.B

_____111.C

_____112.A

_____113.C

_____114.D

_____115.A

_____116.A

_____117.B

_____118.A

_____119.D

_____120.A

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