Geometry Midterm Exam, 2000-01



1. Two segments that have equal lengths are:

A. collinear

B. congruent

C. coplanar

D. perpendicular

Use the diagram to the right to answer questions 2 – 5.

2. In the plane figure shown, (BEC and (BEA are:

A. vertical angles

B. nonadjacent angles

C. complementary angles

D. supplementary angles

3. m(DEB + m(AEB =

A. m(BEC

B. m(AEC

C. m(CED

D. m(AED

4. If m (DEC = 20(, then m (AED =

A. 60 B. 150 C. 110 D. 120

5. If m (1 = 25( and m (CED = 55(, then (1 and (CED are:

A. acute angles B. complementary angles

C. supplementary angles D. obtuse angles

Use the diagram below to answer questions 6 and 7.

6. What is the slope of line AB?

A. ½ B. -½ C. 2 D. –2

7. What is the distance from A to B?

A. 5.5 B. 80 C. 4[pic] D. 2[pic]

Use the diagram and the information below to answer questions 8 – 10.

M N O P Q

MQ = 30, MN = 5, MN = NO, OP = PQ

8. Find the length of OQ

A. 10 B. 15 C. 20 D. 25

9. Find the length of PQ

A. 5 B. 10 C. 15 D. 20

10. Find the midpoint of a segment with endpoints A(-7, 3) and B(3, -3)

A.(-2, -3) B.(-2, 0) C. (–5, 0) D.(2, 0)

11. [pic]bisects (CAD. Find the value of x.

A. 2

B. 4

C. 5

D. 6

12. Which property of equality matches the conditional statement, “If AB = BC and BC = CD, then AB = CD?”

A. Symmetric B. Transitive C. Reflexive D. Addition

13. The converse of the statement “If it is Saturday, then there is no school” is

A. If there is no school, then it is Saturday.

B. There is no school if it is Saturday.

C. When it is Saturday there is no school.

D. There is no school only if it is not Saturday.

14. The converse of q ( r is:

A. r ( q B. (r ( q C. (r ( (q D. none of these

15. In the conditional statement p ( q, the p is called the:

A. hypothesis B. conclusion C. deduction D. converse

16. (K and (J are complementary angles. If m (K = 36(, find m (J.

A. 71( B. 161( C. 90( D. 54(

17. (P and (Q form a linear pair and m (P = 118(. Find m (Q.

A. 62( B. 28( C. 118 ( D. 90(

18. Two angles are supplementary. If one of the angles is 27(, then the other angle is

A. 27( B. 54( C. 63( D. 153(

19. If m(3 = 126(, then m(2 = _______

A. 36(

B. 64(

C. 126(

D. not given

Use the diagram below to answer questions 20 and 21.

20. Solve for x in the diagram.

A. 20 B. 45

C. 48 D. 102

21. Solve for y in the diagram.

A. 20 B. 45

C. 48 D. 102

Match the term with its diagram. Use each letter ONCE.

22. consecutive interior angles

23. corresponding angles

24. alternate interior angles

25. alternate exterior angles

26. same side exterior angles

27. vertical angles

28. linear pair

29. supplementary angles

30. complementary angles

31. right angle

32. A line parallel to y = 2/3 x – 7 is

A. y = -2/3 x + 7

B. y = -2/3 x – 7

C. y = 2/3 x + 1

D. y = 3/2 x + 2

33. The line y = -½ x +3 is perpendicular to which line?

A. y = -½ x + 6

B. y = ½ x + 1

C. y = -2x

D. y = 2x – 3

E.

For exercises 34 – 35, use the diagram below, where lines a and b are parallel.

34. Choose the reason the statement “If m(1 = 85(, then m(5 = 85(” is true.

A. Alternate Int. (s Theorem

B. Alternate Ext.(s Theorem

C. Consecutive Int. (s Theorem

D. Corresponding (s Postulate

35. Choose the reason the statement “If m(3 = 45(, then m(5 = 135(” is true.

A. Alternate Int. (s Theorem

B. Alternate Ext.(s Theorem

C. Consecutive Int. (s Theorem

D. Corresponding (s Postulate

36. What value of x would make lines w and v parallel?

A. 20

B. 40

C. 60

D. 120

37. Which of the statement(s) must be true if a (( b AND x (( y?

I. m(1 = m(6

II. m (3 + m(5 = 180

III. m (7 + m(8 = 180

A. I only

B. II only

C. III only

D. I and III

38. Which lines are parallel?

A. a and b

B. b and c

C. a and c

D. all three lines

39. The sum of all three angles in a triangle is

A.60( B. 90( C. 180( D.360(

40. How many obtuse angles can an isosceles triangle have?

A. 0 B. 1 C. 2 D. 3

41. A triangle with three acute angles and no congruent sides is ______

A. an equiangular triangle

B. a right triangle

C. an acute isosceles triangle

D. an acute scalene triangle

42. A triangle with sides that measure 3 ft, 5 ft, and 5 ft is

A. an equilateral triangle

B. a right triangle

C. an isosceles triangle

D. a scalene triangle

43. The triangle to the right can be classified as

A. acute isosceles

B. acute scalene

C. obtuse isosceles

D. obtuse scalene

44. The measure of one base angle of an isosceles triangle is 63(.

Find the measure of the vertex angle.

A. 54

B. 63

C. 76

D. 128

45. Find the measure of (1.

1 30(

A. 65(

B. 85(

2 90(

46. Find the value of x if (M ( (B and (K ( (C.

A. 29(

B. 40(

C. 43(

D. 58(

E.

47. Find the value of x

A. 57

B. 62

C. 119

D. 237

48.Which postulate or theorem can be used to prove that (ABC ( (BAD?

A. SSS

B. SAS

C. ASA

D. AAS

Use the diagram below to answer questions 49 – 50.

49. What is the value of x and y?

A. x = 70, y = 55

B. x = 55, y = 110

C. x = 70, y = 110

D. x = 70, y = 145

50. What is the value of w and z?

A. w = 145, z = 70

B. w = 110, z = 55

C. w = 110, z = 70

D. w = 145, z = 55

51. Which is the shortest side?

A. AC

B. AB

C. BC

D. a or c

52. List the sides in order from longest to shortest.

A. [pic]

B. [pic]

C. [pic]

D. [pic]

53. If line a is parallel to line b, what is m(1?

A. 40(

B. 50(

C. 90(

D. 140(

54. A ladder is leaning against a house at an angle of 38( as shown in the diagram.

What is the measure of the angle, x, between the ladder and the ground?

A. 38(

B. 42(

C. 52(

D. 142(

55. Lines [pic]and [pic]intersect at P. [pic] is perpendicular to [pic],

and M(APD is 170(.

What is the measure of (DPB?

A. 10(

B. 20(

C. 30(

D. 40(

56. The diagram shows how a periscope works. If the two mirrors are

parallel and (1 ( (3, what is m(6 when m(2 = 90(?

A. 30(

B. 45(

C. 50(

D. 60

57. Using the information on the diagram, which is true?

A. [pic](( [pic][pic]

B. [pic](( [pic]

C. [pic] (( [pic]

D. [pic] (( [pic]

58. Line a is parallel to line b if –

A. m(4 = m(2

B. m(3= m(5

C. m(4 = m(5

D. m(3= m(2

59. Triangle ABC is a right triangle with the right angle at C.

Which are possible measures for angle A and angle B?

A. 48( and 50(

B. 38( and 32(

C. 52( and 38(

D. 52( and 128(

60. On the shores of a river, surveyors marked locations A, B, and C.

The measure of (ACB = 70(, and the measure of (ABC = 65(.

Which lists the distances between these locations in order, from least to greatest?

A. A to B, B to C, A to C

B. B to C, A to B, A to C

C. B to C, A to C, A to B

D. A to C, A to B, B to C

61. Three lookout towers are located at points A, B, and C on the section

of a national forest shown in the drawing.

Which of the following statements is true concerning (ABC formed by the towers?

A. m(A is greatest.

B. m(C is greatest.

C. m(A is least.

D. m(C is least.

62. The figure has angle measures as shown.

What is the measure of (BCD?

A. 120(

B. 80(

C. 60(

D. 30(

| | | | |

|Question Answer | |Question |Answer |

|1 B | |32 |C |

|2 C | |33 |D |

|3 D | |34 |D |

|4 C | |35 |C |

|5 A | |36 |A |

|6 B | |37 |D |

|7 C | |38 |A |

|8 C | |39 |C |

|9 B | |40 |B |

|10 B | |41 |D |

|11 D | |42 |C |

|12 B | |43 |C |

|13 A | |44 |A |

|14 A | |45 |C |

|15 A | |46 |A |

|16 D | |47 |B |

|17 A | |48 |C |

|18 D | |49 |C |

|19 C | |50 |D |

|20 A | |51 |A |

|21 B | |52 |D |

|22 C | |53 |A |

|23 A | |54 |C |

|24 E | |55 |A |

|25 B | |56 |B |

|26 D | |57 |D |

|27 E | |58 |C |

|28 D | |59 |C |

|29 C | |60 |C |

|30 B | |61 |A |

|31 A | |62 |C |

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