Download A. 4 B. 6 C. 33 D. 35

Name: _________________________
Midterm Review – Geometry
PART I. True or False.
If the statement is FALSE, write the word or phrase that will make the statement TRUE.
1. It is possible to have a triangle with sides of 10, 8, and 8.
True
2. In a triangle, the largest angle is opposite the longest side.
True
3. If the measure of one acute angles of a right triangle is 54, then the other acute angle is 46.
False: 36
4. If AM = MB, then M must be the midpoint of AB.
False; must be between A & B
5. When two parallel lines are cut by a transversal, corresponding angles are complementary.
False; 
6. If the legs of a right triangle are congruent, then each acute angle has a measure of 45.
True
7. Corresponding parts of congruent triangles are congruent.
True
8. Coplanar points are also collinear.
False; Collinear are Coplanar but not all coplanar are collinear
9. An equilateral triangle is isosceles.
True
10. On a line, if A is between B and C, then AB + BC = AC.
False; BA + AC = BC
11. An obtuse triangle has three obtuse angles.
False; one
12. SSA is a method to prove a triangle congruent.
False; ASA, AAS, HL, SSS, SAS would work but not SSA
13. The intersection of two planes is a line.
True
14. The slopes of parallel lines are negative reciprocals of each other.
False; congruent
15. Acute angles are less than or equal to 90.
False; less than
16. All equiangular triangles are equilateral.
True
17. If two lines have the same slope, then the lines are parallel.
True
18. If two lines intersect, then they intersect at a point.
True
19. The acute angles in a right triangle are supplementary.
False; Complementary
20. If two angles are supplements of congruent angles, then the two angles are congruent.
True
21. All right triangles are congruent.
False
22. A right triangle has at least one right angle.
True
23. The hypotenuse of a right triangle is the side adjacent to the right angle.
False; Across
24. All alternate interior angles are supplementary.
False; congruent
25. The base angles of an isosceles triangle are complementary.
False; congruent
26. Skew lines are coplanar lines that do not intersect.
False; not coplanar and don not intersect
27. The slope of a vertical line is zero.
False ; undefined
28. The legs of an isosceles triangle are equal in length.
True
29. Two angles are complementary if the sum of their measures is 90.
True
30. The sum of the measures of the angles in a triangle is 360.
False; 180
31. Adjacent angles form a linear pair.
False; Supplementary and Adjacent
32. AA is a method to prove triangles congruent.
False; Similar
33. An isosceles triangle has at least two congruent sides.
True
34. If a conditional statement is false, then so is its converse.
False; Contrapositive
35. A scalene triangle has no congruent sides.
True
36. The hypotenuse of a right triangle is the side opposite the right angle.
True
37. The segment connecting the midpoints of the two sides of a triangle is parallel to the third side and
half as long.
True
38. The leg of a right triangle is the longest side.
False; hypotenuse
39. Two triangles are congruent if corresponding angles are congruent.
False; Similar
40. The contrapositive of the statement: “If a triangle is isosceles, then it has at least two congruent sides”
is “If a triangle does not have at least two congruent sides, then it is not isosceles.”
True
41. Vertical angles are congruent.
True
C
PART II. Multiple Choice.
42. Plane X contains:
A. CE
B. Point C
X
C. Point D
43. Two segments that have equal length are:
A. collinear
B. congruent
D. EB
E
B
D
C. coplanar
D. perpendicular
44. On a number line, the distance between two points with coordinates –15 and 9 is:
A. 6
B. –6
C. 23
D. –23
45. The statement “If mA = mB, then mB = mA” illustrates which property:
A. reflexive
B. symmetric
C. transitive
D. commutative
46. In the conditional statement p  q , the q is called the:
A. hypothesis
B. conclusion
C. deduction
47. The inverse of the statement “If it is snowing, then there is no school” is
A. If there is no school, then it is snowing.
B. There is no school if it is snowing.
C. If it is not snowing, then there is school.
D. There is no school only if it is not snowing.
48. The vertex of TRS is:
A. R
B. S
C. T
D. unknown
D. converse
49. In the plane figure shown, 1 and 2 are:
A. vertical angles
B. nonadjacent angles
C. complementary angles
D. supplementary angles
50. mDEB + mAEB =
A. mBEC
B. mAEC
C. mCED
D. mAED
51. If EB bisects AEC, then mCEB =
A. 45
B. 90
C. mDEC
D. mAEC
52. If m DEC = 35, then m AED =
A. 55
B. 145
C. 125
D. 155
53. If m 1 = 32 and m CED = 58, then 1 and CED are:
A. vertical angles
B. complementary angles
C. supplementary angles
D. obtuse angles
Use the diagram on the right to answer questions 54-56.
54. If j k, then 8 is congruent to:
A. 7
B. 3
C.  2
D.  1
55. If j k and t  k, then m1 =
A. m2
B. m3
C. m4
4
1 3
2
D. all three
56. If j  k and m2 = 115, then 6 is:
A. acute
B. right
C. obtuse
57. The number of right angles in a right triangle is:
A. 0
B. 1
C. 2
6
5 7
8
D. unknown
D. 3
58. The distance between (3, 5) and (9, -3) is:
A. 100
B.
2 37
C.
2 35
D. 10
b4,6gand b2,8gis:
4,4g
3,1g
C. b
D. b
59. The midpoint of the segment with endpoints
A.
b6,2g
B.
b2,2g
60. In TQR, m T = 65 and m Q = 35, then m QRT =
A. 80
B. 100
C. 10
D. 110
61. Determine which set of numbers can be the measure of the sides of a triangle.
A. 7, 4, 3
B. 15, 11, 4
C. 24, 68, 43
D. 16, 18, 11
62. If m1 = 105, then m4 =
A. 105
B. 75
C. 95
D. 65
63. Which of the following can NOT be used to prove that two triangles are congruent?
A. SSS
B. SSA
C. SAS
D. AAS
64. ABE  CBE. In CBA which part of ABE corresponds to BEC?
A. A
B. EBA
C. BCE
D. BEA
For #65-68, Use the diagram to determine the method that can be used to prove ABCEDC.
65. Given BD; BC  DC.
A. SSS
B. SAS
C. ASA
D. AAS
66. Given BC  DC; AC  EC.
A. AAS
B. SSS
C. SAS
D. ASA
67. Given A and E are right angles, BC  DC.
A. HL
B. AAS
C. SSS
D. SSA
68. Given AB  DE, AC  EC and A and E are right angles.
A. AAS
B. SSS
C. SAS
D. HL
69. The measure of one base angle of an isosceles triangle is 47. Find the measure of the vertex angle.
A. 86
B. 47
C. 106
D. 53
70. In isosceles DEF, DE = EF. If DE = 3x – 6, DF = 2x + 2, and EF = x + 4, find the length of DF.
A. 7
B. 9
C. 12
D. 5
71. K and J are complementary angles. If m K = 54, find m J.
A. 71
B. 161
C. 90
D. 36
72. P and Q form a linear pair and m P = 62. Find m Q.
A. 62
B. 28
C. 118
D. 90
73. Identify the if-then form of “All tigers are cats.”
A. If the animal is a tiger, then it is a cat.
B. If the animal is a cat, then it is a tiger.
C. If the animal is not a cat, then it is not a tiger.
D. If the animal is not a tiger, then it is not a cat.
74. In ABC, m A = 60 and m ACB = 70. What is the longest side of ABC?
A. unknown
B. AC
C. BC
D. AB
k
Use the figure on the right for questions 75 – 78.
Write the answer in the blank provided.
j
1 2
4 3
75. 8 and 6 are _______________
A. complementary
B. congruent
C. unknown
D. supplementary
5
8 6
7
9
12 10
11
76. If k  j and m2 = 72, then m4 = _______________
A. 108
B. 72
C. 180
D. 910
77. If k j, m9 = 9x + 5, and m8 = x + 35, then x = __________
A. 140
B. 5
C. 14
D. 180
78. Given m10 = 5x + 2 and m6 = 3x + 28, find x so that k  j.
A. 13
B. 12
C. 9
D. 8
79. The measures of two angles of a triangle are 32 and 47. What is the measure of the third angle?
A. 79
B. 109
C. 180
D. 101
80. Find the values of x and y so that ABC  DEF by HL.
A. x=45, y=12
B. x=45, y=5
C. x=90, y=12
D. x=90, y=13
81. Two sides of a triangle have lengths 14 and 19. Which measurement could be the measure of the
third side?
A. 4
B. 6
C. 33
D. 35
82. What conclusion is justified by the following statements: “If I get a job, then I will save money.” and
“If I save money, then I will buy a car.”?
A. If I get a job, then I will buy a car.
B. If I buy a car, then I will get a job.
C. I can buy a car, if I get a job.
D. If I save my money, then I will buy a car.
83. The contrapositive of r  q is:
A. r  q
B. r  q
C. r  q
D. none of these
84. The lengths of the legs of an isosceles triangle are 3x and x + 12. Find x.
A. 18
B. 12
C. 6
D. 4
85. An angle has a measure of x. Its complement has a measure x + 10. Find x.
A. 80
B. 45
C. 50
D. 40
86. An angle and its supplement have measures x + 20 and x – 20. Find the measure of each angle.
A. 90o and 90o
B. 80o and 100o
C. 120o and 60o
D. 110o and 70o
87. Find the distance between A
A.
18
B. 3
b3,4gand C b7,2g. Reduce to simplest radical form.
6
C.
168
D. 2
34
88. In the figure, if AD = 50, CD = 12, and B is the midpoint of AC, find BC.
A. 38
•
•
•
•
A
B
C
D
B. 19
C. 25
D. 37
89. What is the slope of the line that passes through the points (-4, 8) and (3, -7)?
A.
7
15
B.
15
7
C. -
15
7
D.
1
7
90. Find the slope of the line perpendicular to the line containing points (4,5) and (-2,3).
A. ½
B. –1/3
C. -3
D. 1/3
91.
List the sides of STU in order from LONGEST to SHORTEST if the angles of STU have the
indicated measures: m S = x + 6; m T = 2x + 8; and m U = 3x –2.
A. ST-SU-TU
B. TS-UT-SU
C. US-UT-ST
D. TU-US-ST
92.
The measures of two vertical angles are 5x–15 and 3x+3. Find x.
A. 14
B. 16
C. 12
D. 9
93.
The measures of the angles of a triangle are x – 15, x, and x + 15. Find x.
A. 60
B. 55
C. 65
D. 45
94. The side opposite the right angle in a right triangle is called the________________________.
A. base
B. vertex
C. hypotenuse
D. leg
95. A triangle with no congruent sides is called a(n) ______________ triangle.
A. equiangular
B. isosceles
C. obtuse
D. scalene