Download GEOMETRY CP MIDTERM EXAM

CP Geometry Midterm Review
1
Match each definition with the correct term.
1 __________
Acute Angle
A
Two lines that are not coplanar and do
not intersect
2 __________
Obtuse Angle
B
Ray or segment that splits an angle into
two equal halves
3__________
Adjacent Angles
C
An angle greater than 90° and less than
180°
4 __________
Linear Pair
D
A triangle with (at least) two equal sides.
5 __________
Complementary Angles
E
A pair of non-adjacent angles formed by
the intersection of two straight lines.
These angles are always congruent.
6 __________
Vertical Angles
F
A set of points, lines, line segments, rays
or any other geometrical shapes that lie
on the same plane
7 __________
Supplementary Angles
G
An angle greater than 0° and less than
90°
8 __________
Angle Bisector
H
3 or more points on the same line
9 __________
Isosceles Triangle
I
Two angles that are adjacent and
supplementary
10 __________ Obtuse Triangle
J
Two angles whose sum is 180
11__________
Skew Lines
K
Triangle with one obtuse angle.
12__________
Coplanar
L
Two angles that share a common side
and vertex and no common interior
points
13_________
Collinear
M Two angles whose sum is 90
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CP Geometry Midterm Review
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14 . Name this angle in 3 different ways.
15. Find mÐNLM if mÐNLM = (2x+9), mÐKLM =
52 and mÐNLK =75.
N
M
K
16.
What is the vertex of ∠DEF?
17.
What is the complement of 50 ° angle?
18.
What is the supplement of 50 ° angle?
L
Questions 19 and 20 refer to the diagram to the right.
19. If 𝑚∠2 = 110° and 𝑚∠4 =(5x + 30) , then the
value of x is ____.
2
1
3
4
20. If mÐ1 = 60  and mÐ2 = (3x + 15) , then the
value of x is _____.
21. SQ bisects ÐRST . Find the measure of ÐQST if
mÐRST = 50.
T
Q
S
R
22. Write the converse of: "If two segments have the same measure, then they are congruent."
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CP Geometry Midterm Review
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23. In the diagram to the right,
find 𝑚∠1 and 𝑚∠2.
130°
80°
Use the diagram to answer questions 24-25.
r
24. If r s , Ð3then is congruent to ________.
b
9
1 2
4 3
c
25. If∠8 ≅ ∠16, then ________.
s
5 6
8 7
10
11
12
13 14
16 15
Use the diagram to answer questions 26-27
26. If b c , then ∠4 must be ________ to ∠5
r
27. If c b, then ∠2 is congruent to ________.
b
c
28. Find x if AB CD , 𝑚∠7= (5x+60), and 𝑚∠1 =70.
A
9
1 2
4 3
10
11
12
5 6
8 7
13 14
16 15
B
2
1
3
C
s
4
5
D
6
7
8
29. What are the measures of the angles in an equilateral triangle?
30. If two angles of a triangle have measures 25 and 75, what is the measure of the
third angle?
31. How many rights angles can any given triangle have?
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CP Geometry Midterm Review
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32. Use the markings on the diagram to determine why
ADB @ CDB .
C
B
D
A
33. If
PQR @
DBF (not shown), then ̅̅̅̅
𝐵𝐷 ≅ ______.
34. Determine what information you would need to know in
order to use the ASA Postulate to show that the triangles are
congruent. ≅
A
D
B
C
35. In JKL (not shown), KL @ JL , mÐK = 70, mÐL = 40. Find mÐJ .
Hint – Draw triangle to help solve.
36. If
ABC @ DEF , then you can say AB ≅ DE because ____________.
37. Given
ABC @ XYZ , BC=40 and YZ =5x+10, find the value of x.
38. Name the 5 ways of proving a triangle congruent.
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CP Geometry Midterm Review
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For questions 39-40, state which of the postulates or theorems could be used to justify the
conclusion.
̅̅̅̅ and E is the midpoint of 𝐷𝐺
̅̅̅̅ , then ∆𝐷𝐻𝐸 ≅
̅̅̅̅ ⊥ 𝐷𝐺
39. If 𝐻𝐸
∆𝐺𝐻𝐸 by ___________.
40. If ̅̅̅̅
𝐻𝐺 = ̅̅̅̅
𝐻𝐷 and ̅̅̅̅
𝐷𝐸 = ̅̅̅̅
𝐸𝐺 , then ∆𝐷𝐻𝐸 ≅ ∆𝐺𝐻𝐸
by ___________.
41. Name the additional pairs of
corresponding parts that need to be
congruent in order to prove that
∆VUW ≅ ∆YXZ by ASA.
42. The base angles of an isosceles triangle are always _____________.
43. Find mÐ2 .
70°
30°
44. Find mÐ3
3
2
1
45. Find mÐ1
B
46. Which segment is an altitude of
47. Which segment is a median of
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ABC ?
E
A
ABC ?
5
C
D
CP Geometry Midterm Review
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48. If two sides of a triangle have the following measures, find the range of possible measures
for the third side. 4, 8
49. Determine if the three numbers can be measures of the sides of a triangle. 4, 7, 8?
50. Determine if the three numbers can be measures of the sides of a triangle. 8, 11, 22?
51. If D is the midpoint of ̅̅̅̅
𝐴𝐵 and E is the
̅̅̅̅
̅̅̅̅ = 12.
midpoint of 𝐴𝐶 find the length of ̅̅̅̅
𝐷𝐸 . 𝐵𝐶
52. If
6+𝑥
𝑥
=
8
2
, then what is the value of x?
̅̅̅̅ = 8.4,
53. Δ𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐹, if ̅̅̅̅
𝐴𝐵 = 6, ̅̅̅̅
𝐴𝐶 = 8, 𝐵𝐶
̅̅̅̅ = 5.4, what is the measure of ̅̅̅̅
𝑎𝑛𝑑 𝐷𝐹
𝐷𝐸 .
54. If b = 6 and c = 10, what is the length of a?
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CP Geometry Midterm Review
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Classify the triangles in numbers 67 – 69 as acute, obtuse or right.
55. 6, 7, 8
56. 6, 8, 10
57. 9, 12, 17
Find the value of x and y.
58. x =
B
y
60°
7
59. y =
30°
C
x
A
Find the value of a and b.
60. a =
45°
b
61. b =
5
a
62. What is the sum of the exterior angles in a convex 12-sided polygon?
63. What is the sum of the interior angles of a 12- sided polygon?
64. What is the measure of each angle of a regular 8-sided polygon?
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CP Geometry Midterm Review
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Use the diagram for problems 65-67.
65. What is the scale factor of AXYZ to ABCD? (1.3.1.2)
C
13
B
A. 2:3
B. 5:2
C. 1:3
D. 4:16
8
16
Y
X
66. Find YZ. (1.3.1.2)
A. 5 1/3 B. 32
4
C. 8
A
D. 12/64
D
Z
15
67. What is the ratio of their perimeters? (1.3.1.2)
A. 2:3
B. 1:3
C. 4:26
D. 4:9
68. ABC ~ XYZ. AB = 5 inches and XY = 15 inches. If the perimeter of
inches, then what is the perimeter of ABC? (1.3.1.1)
XYZ is 48
69. State whether or not the figure is a polygon. If it is, classify it as convex or concave.
a.
b.
c.
d.
70. Identify the polygon by its number of sides. Then determine if it appears to be regular, why
or why not.
a.
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b.
c.
8
d.
CP Geometry Midterm Review
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71. The measures of six interior angles of a heptagon are 111, 110, 121, 135, 139, and 92. Find
the measure of the seventh interior angle.
Determine whether the quadrilateral is a parallelogram.
If yes, give a reason for your answer.
72.
73.
Use the rectangle below to answer #74-76.
74. Find the measure of segment BC.
75. Find the measure of angel ABC.
76. Find the measure of segment BE.
77.
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78.
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