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

23

Geometry - Final Review

____ 1. Name the line and plane shown in the diagram.

A. QP

and plane SR C. PQ

and plane SP

B. PQ

and plane PQS D. line P and plane PQS

____ 2. Are points C, G, and H collinear or noncollinear?

A. noncollinear B. collinear C. impossible to tell

____ 3. Are M , N , and O collinear? If so, name the line on which they lie.

A. Yes, they lie on the line N P.

B. Yes, they lie on the line M P.

C. Yes, they lie on the line MO.

D. No, the three points are not collinear.

Name: ________________________ ID: A

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____ 4. What is the intersection of plane STXW and plane SVUT?

A. SV

B. ST

C. YZ

D. TX

____ 5. If EF 2x 12, FG 3x 15, and EG 23, find the values of x, EF, and FG. The drawing is not to scale.

A. x = 10, EF = 8, FG = 15 C. x = 10, EF = 32, FG = 45

B. x = 3, EF = –6, FG = –6 D. x = 3, EF = 8, FG = 15

____ 6. What segment is congruent to AC?

A. BD B. BE C. CE D. none

____ 7. If Z is the midpoint of RT , what are x, RZ, and RT?

A. x = 18, RZ = 134, and RT = 268 C. x = 20, RZ = 150, and RT = 300

B. x = 22, RZ = 150, and RT = 300 D. x = 20, RZ = 300, and RT = 150

____ 8. Which point is the midpoint of AE?

A. D B. B C. not B, C, or D D. C

Name: ________________________ ID: A

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____ 9. Complete the statement.The drawing is not to scale.

If mGDF 54º, then mEDF ? .A. 27 C. 63

B. 54 D. none of these

____ 10. How are the two angles related?

A. supplementary C. vertical

B. adjacent D. complementary

____ 11. The complement of an angle is 53°. What is the measure of the angle?A. 37° B. 137° C. 47° D. 127°

____ 12. 1 and 2 are a linear pair. m1 x 15, and m2 x 77. Find the measure of each angle.A. 1 59, 2 131 C. 1 44, 2 146

B. 1 44, 2 136 D. 1 59, 2 121

Name: ________________________ ID: A

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____ 13. Find the coordinates of the midpoint of the segment whose endpoints are H(6, 4) and K(2, 8).A. (4, 4) B. (2, 2) C. (8, 12) D. (4, 6)

____ 14. M is the midpoint of CF for the points C(3, 7) and F(5, 5). Find MF.A. 2 B. 2 2 C. 2 D. 4

____ 15. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.A. 11 B. 7.8 C. 61 D. 14.9

____ 16. The Frostburg-Truth bus travels from Frostburg Mall through the city’s center to Sojourner Truth Park. The mall is 4 miles east and 5 miles north of the city’s center. Truth Park is 4 miles west and 2 miles south of the city’s center. How far is it from Truth Park to the mall to the nearest tenth of a mile?A. 10.6 miles B. 4.5 miles C. 6.4 miles D. 3 miles

____ 17. Find the perimeter of the rectangle. The drawing is not to scale.

A. 95 feet B. 190 feet C. 124 feet D. 161 feet

____ 18. Find the circumference of the circle to the nearest tenth. Use 3.14 for .

A. 78.5 m B. 314 m C. 1962.5 m D. 157 m

____ 19. If the perimeter of a square is 140 inches, what is its area?A. 1225 in. 2 B. 35 in. 2 C. 19,600 in. 2 D. 140 in. 2

Name: ________________________ ID: A

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____ 20. Find the area of the circle in terms of .

A. 42 in.2 B. 1764 in.2 C. 441 in.2 D. 84 in.2

____ 21. Write an expression that gives the area of the shaded region in the figure below. You do not have to evaluate the expression. The diagram is not to scale.

A. A 12 13 4 6 C. A (13 6) (12 4)

B. A (13 4) (12 6) D. A 12 13 (12 4) (13 6)

Name: ________________________ ID: A

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____ 22. Complete the two-column proof.

Given: 12x 6y 5; x 5

Prove: 656 y

12x 6y 5; x 5 a. ________

60 6y 5 b. ________

6y 65 c. ________

y 656 d. ________

656 y e. ________

A. a. Givenb. Substitution Propertyc. Addition Property of Equalityd. Division Property of Equalitye. Symmetric Property of Equality

C. a. Givenb. Symmetric Property of Equalityc. Addition Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

B. a. Givenb. Substitution Propertyc. Addition Property of Equalityd. Addition Property of Equalitye. Symmetric Property of Equality

D. a. Givenb. Substitution Propertyc. Addition Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

____ 23. What is the value of x?

A. –16 B. 120 C. 60 D. 16

Name: ________________________ ID: A

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____ 24. Find the values of x and y.

A. x = 15, y = 17 C. x = 68, y = 112

B. x = 112, y = 68 D. x = 17, y = 15

25. What is the value of x? Justify each step.AC 32

AB BC AC a. ____

2x 6x 8 32 b. ____

8x 8 32 c. ____

8x 24 d. ____

x 3 e. ____

Name: ________________________ ID: A

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____ 26. Line r is parallel to line t. Find m6. The diagram is not to scale.

A. 32 B. 138 C. 142 D. 42

____ 27. Find mG. p r. The diagram is not to scale.

A. 34 B. 110 C. 104 D. 146

____ 28. Find the values of x and y. The diagram is not to scale.

A. x = 51, y = 63 C. x = 63, y = 77

B. x = 77, y = 63 D. x = 77, y = 65

Name: ________________________ ID: A

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____ 29. Find the values of x, y, and z. The diagram is not to scale.

A. x 63, y 104, z 76 C. x 63, y 76, z 104

B. x 76, y 63, z 104 D. x 76, y 104, z 63

____ 30. Find the value of x. The diagram is not to scale.

A. 33 B. 162 C. 147 D. 75

____ 31. Find the value of x. The diagram is not to scale.

A. 33 B. 70 C. 23 D. 13

Name: ________________________ ID: A

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____ 32. A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

A. 99 B. 91 C. 81 D. 105

____ 33. What is the slope of the line shown?

A. 136 C. 5

11

B. 512 D. 11

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____ 34. Write an equation in slope-intercept form of the line through point P(6, –1) with slope 4.A. y = 4x – 1 C. y + 1 = 4(x – 6)

B. y = 4x – 25 D. y + 6 = 4(x – 1)

Name: ________________________ ID: A

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____ 35. Write an equation in slope-intercept form of the line through points S(–7,–6) and T(10,8).

A. y 1417x – 4

17 C. y = 1417x + 4

17

B. y 1417x + 4

17 D. y = 1417x – 4

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____ 36. Write the equation for the vertical line that contains point E(–7, 7).A. y = 7 B. x = –7 C. y = –7 D. x = 7

____ 37. What is the equation in point-slope form for the line parallel to y = 5x – 4 that contains P(–6, 1)?A. x – 1 = –5(y + 6) C. y – 1 = –5(x + 6)

B. y + 1 = 5(x + 6) D. y – 1 = 5(x + 6)

____ 38. What is an equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8, –4)?

A. y + 4 = 12(x – 8) C. y + 4 = 2(x – 8)

B. x + 4 = 2(y – 8) D. y + 8 = 12(x – 4)

39. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.

____ 40. If BCDE is congruent to OPQR, then DE is congruent to ? .A. PQ B. OR C. OP D. QR

____ 41. Given QRS TUV, QS 3v 2, and TV 7v 6, find the length of QS and TV.A. 2 B. 9 C. 8 D. 20

Name: ________________________ ID: A

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____ 42. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale.

A. 4 B. 5 C. 3 D. 38

____ 43. Justify the last two steps of the proof.Given: RS UT and RT USProve: RST UTS

Proof:1. RS UT 1. Given2. RT US 2. Given3. ST TS 3. ?4. RST UTS 4. ?

A. Symmetric Property of ; SSS C. Reflexive Property of ; SSS

B. Reflexive Property of ; SAS D. Symmetric Property of ; SAS

Name: ________________________ ID: A

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____ 44. State whether ABC and AED are congruent. Justify your answer.

A. yes, by either SSS or SAS

B. yes, by SSS only

C. yes, by SAS only

D. No; there is not enough information to conclude that the triangles are congruent.

____ 45. If A D and C F, which additional statement does NOT allow you to conclude that ABC DEF?

A. BC EF C. AC DF

B. B E D. AB DE

Name: ________________________ ID: A

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____ 46. Based on the given information, what can you conclude, and why?Given: H L, HJ JL

A. HIJ LKJ by ASA C. HIJ JLK by ASA

B. HIJ JLK by SAS D. HIJ LKJ by SAS

____ 47. What is the value of x?

A. 86.5° B. 43.25° C. 133.25° D. 46.75°

____ 48. Find the value of x. The diagram is not to scale.

Given: RS ST , mRST 7x 54, mSTU 8x

A. 14 B. 152 C. 16 D. 19

Name: ________________________ ID: A

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____ 49. Find the values of x and y.

A. x 44, y 46 C. x 90, y 44

B. x 46, y 44 D. x 90, y 46

____ 50. Find the value of x. The diagram is not to scale.

A. x 60 B. x 21 C. x 15 D. none of these

____ 51. The octagon in the figure is equiangular and AB AC. Find mACB.

A. 135 B. 45 C. 30 D. 90

Name: ________________________ ID: A

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____ 52. What additional information will allow you to prove the triangles congruent by the HL Theorem?

A. A E C. AC DC

B. mBCE 90 D. AC BD

____ 53. What common angle do CDG andFCE share?

A. C C. E

B. F D. D

____ 54. Find the length of the midsegment. The diagram is not to scale.

A. 24 B. 0 C. 42 D. 84

Name: ________________________ ID: A

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____ 55. Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale.

A. 52 B. 26 C. 104 D. 38

____ 56. The length of DE is shown. What other length can you determine for this diagram?

A. DF = 12 C. DG = 6

B. EF = 6 D. No other length can be determined.

____ 57. DF

bisects EDG. Find the value of x. The diagram is not to scale.

A. 285 B. 419 C. 32 D. 19

Name: ________________________ ID: A

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____ 58. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale.

A. 2 B. 12 C. 14 D. 24

____ 59. In ACE, G is the centroid and BE = 18. Find BG and GE.

A. BG 6, GE 12 C. BG = 412 , GE = 131

2

B. BG 12, GE 6 D. BG = 9, GE = 9

Name: ________________________ ID: A

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____ 60. What is the orthocenter of the triangle with two altitudes given by the lines x 1 and y x 1?

A. (0,1) C. (1,2)

B. (1,0) D. none of these

____ 61. Name the smallest angle of ABC. The diagram is not to scale.

A. A

B. B

C. C

D. Two angles are the same size and smaller than the third.

Name: ________________________ ID: A

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____ 62. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by 1 and 2 is 11 cm, the side included by 2 and 3 is 16 cm, and the side included by 3 and 1 is 14 cm.

A. 3 B. 4 C. 2 D. 1

____ 63. Which three lengths could be the lengths of the sides of a triangle?A. 12 cm, 5 cm, 17 cm C. 9 cm, 22 cm, 11 cm

B. 10 cm, 15 cm, 24 cm D. 21 cm, 7 cm, 6 cm

____ 64. Two sides of a triangle have lengths 6 and 17. Which expression describes the length of the third side?A. at least 11 and less than 23 C. greater than 11 and at most 23

B. at least 11 and at most 23 D. greater than 11 and less than 23

____ 65. What is the range of possible values for x?The diagram is not to scale.

A. 12 x 48 C. 10 x 50

B. 0 x 10 D. 10 x 43

Name: ________________________ ID: A

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____ 66. What is the sum of the angle measures of a 35-gon?

A. 5940 B. 6660 C. 6120 D. 6300

____ 67. What is the measure of one angle in a regular 30-gon?

A. 192 B. 84 C. 168 D. 5040

____ 68. Find the missing values of the variables. The diagram is not to scale.

A. x = 74, y = 103 C. x = 93, y = 74

B. x = 74, y = 93 D. x = 103, y = 119

____ 69. Find mA. The diagram is not to scale.

A. 107 B. 117 C. 63 D. 73

Name: ________________________ ID: A

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____ 70. Find the values of the variables in the parallelogram. The diagram is not to scale.

A. x 53, y 31, z 96 C. x 31, y 53, z 96

B. x 53, y 53, z 127 D. x 31, y 53, z 127

____ 71. For the parallelogram, if m2 4x 20 and m4 3x 11, find m1. The diagram is not to scale.

A. 9 B. 16 C. 164 D. 174

____ 72. In the figure, the horizontal lines are parallel and AB BC CD. Find JM. The diagram is not to scale.

A. 27 B. 36 C. 9 D. 18

Name: ________________________ ID: A

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____ 73. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.

A. x = 8, y = 6 B. x = 6, y = 8 C. x = 8, y = 17 D. x = 8, y = 10

____ 74. In the rhombus, m1 15x, m2 x y, and m3 30z. Find the value of each variable. The diagram is not to scale.

A. x = 12, y = 84, z = 6 C. x = 6, y = 84, z = 3

B. x = 12, y = 174, z = 3 D. x = 6, y = 174, z = 6

____ 75. In rectangle PQRS, PR = 18x – 28 and QS = x + 380. Find the value of x and the length of each diagonal.

A. x = 24, PR = 202, QS = 202 C. x = 24, PR = 404, QS = 404

B. x = 12, PR = 392, QS = 392 D. x = 25, PR = 422, QS = 422