Basic 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
Last Update 01/5/12
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Basic Geometry Midterm Review
2
Use the diagram below and to the right for questions 14-16.
Q
14.Which one the following is another name for AH ?
D
B
K
C
A
15. Name a ray opposite AD
16.The intersection of plane P and plane Q is _____.
H
G
17. Draw segment BC ?
18 . Name this angle in 3 different ways.
19. Find mÐNLM and mÐKLM , if mÐNLM = (2x+9),
mÐKLM = 52 and mÐNLK =75.
N
M
K
20.
What is the vertex of ∠𝐷𝐸𝐹?
21.
What is the complement of 50 ° angle?
22.
What is the supplement of 50 ° angle?
L
Questions 23 and 24 refer to the diagram to the right.
23. If 𝑚∠2 = 110° and 𝑚∠4 =(5x + 30) , then the
value of x is ____.
1
2
3
4
24. If mÐ1= 60  and mÐ2 = (3x + 15) , then the
value of x is _____.
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P
Basic Geometry Midterm Review
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25. SQ bisects ÐRST . Find the measure of ÐQST if
mÐRST = 50.
T
Q
S
R
26. Which one of the following is the converse of: "If two segments have the same measure,
then they are congruent."
27. In the diagram to the right,
find 𝑚∠1 and 𝑚∠2.
130°
80°
Use the diagram to answer questions 28-29.
r
28. If r s , Ð3then is congruent to ________.
b
9
1 2
4 3
c
29. If∠8 ≅ ∠16, then ________.
s
5 6
8 7
10
11
12
13 14
16 15
Use the diagram to answer questions 30-31.
30. If b c , then ∠4 must be ________ to ∠5
r
31. If c b, then ∠2 is congruent to ________.
b
c
32. Find x if AB CD , 𝑚∠7= (5x+60), and 𝑚∠1 =70.
A
9
1 2
4 3
13 14
16 15
B
2
1
4
5
3
D
6
7
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10
11
12
5 6
8 7
3
C
s
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Basic Geometry Midterm Review
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33. What are the measures of the angles in an equilateral triangle?
34. If two angles of a triangle have measures 25 and 75, what is the measure of the
third angle?
35. How many rights angles can any given triangle have?
36. Use the markings on the diagram to determine why
ADB @ CDB .
C
B
A
37. If
PQR @
D
𝐵𝐷 ______.
DBF (not shown), then ̅̅̅̅
38. 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
39. In JKL (not shown), KL @ JL , mÐK = 70, mÐL = 40. Find mÐJ .
Hint – Draw triangle to help solve.
40. If
𝐴𝐵 ≅ ̅̅̅̅
𝐷𝐸 because ____________.
ABC @ DEF , then you can say ̅̅̅̅̅̅̅̅̅̅̅̅
41. Given
ABC @ XYZ , BC=40 and XY=5x+10, find the value of x.
42. Name the 5 ways of proving a triangle congruent.
For questions 43-46, state which of the postulates or theorems could be used to justify the
conclusion.
̅̅̅̅ and E is the midpoint of 𝐷𝐺
̅̅̅̅ , then ∆𝐷𝐻𝐸 ≅
̅̅̅̅ ⊥ 𝐷𝐺
43. If 𝐻𝐸
∆𝐺𝐻𝐸 by ___________.
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Basic Geometry Midterm Review
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̅̅̅̅ = 𝐻𝐷
̅̅̅̅ , then ∆𝐷𝐻𝐸 ≅ ∆𝐺𝐻𝐸
̅̅̅̅ and ̅̅̅̅
44. If 𝐻𝐺
𝐷𝐸 = 𝐸𝐺
by ___________.
T
45. Name the additional pairs of
corresponding parts that need to be
congruent in order to prove that
FIG @ TOM by ASA.
F
O
G
I
M
46. The base angles of an isosceles triangle are always _____________.
47. Find mÐ2 .
70°
30°
48. Find mÐ3
3
2
1
49. Find mÐ1
B
50. Which segment is an altitude of
51. Which segment is a median of
Last Update 01/5/12
ABC ?
ABC ?
E
A
5
C
D
Basic Geometry Midterm Review
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For questions 54-59, choose the option that specifies the statement or reason in the
following proof:
B
^
Given: BD
AC
D is the midpoint of AC
Prove:
A
C
Proof:
D
Statements
1.
2.
3.
4.
5.
6.
7.
BD
Reasons
^ AC
ADB ≅ CDB
D is the midpoint of AC
AD = DC
BD @ DB
D ABD @ __________{Q55} __________
∠𝐴 ≅ ∠𝐶
52. A. def. of midpoint
53. A. def. of right
B. Given
Ð B. def of ^ lines
1.
2.
3.
4.
7.
8.
9.
Given
__________{Q52} __________
Given
__________{Q53} __________
__________{Q54} __________
__________{Q56} __________
__________{Q57} __________
C. def of ^ lines
D. def of segment
C def. of midpoint
D. def of vertical Ð ’s
54. A. Reflexive Prop. B. Symmetric Prop. C. def of
@ segments
C. ∆𝐴𝐵𝐶
D. def. of midpoint
55.
A.∆𝐷𝐶𝐵
B. ∆𝐶𝐵𝐷
D. ∆𝐵𝐶𝐷
56.
A. SSS Post.
B. SAS Post.
C. ASA Post.
D. CPCTC
57.
A. SSS Post.
B. SAS Post.
C. ASA Post.
D. CPCTC
58. If two sides of a triangle have the following measures, find the range of possible measures
for the third side. 4, 8
59. Determine if the three numbers can be measures of the sides of a triangle. 4, 7, 8?
60. Determine if the three numbers can be measures of the sides of a triangle. 8, 11, 22?
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Basic Geometry Midterm Review
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61. If D is the midpoint of ̅̅̅̅
𝐴𝐵 and E is the
̅̅̅̅ find the length of ̅̅̅̅
̅̅̅̅ = 12.
midpoint of 𝐴𝐶
𝐷𝐸 . 𝐵𝐶
62. If
6+𝑥
𝑥
8
= 5, then what is the value of x?
̅̅̅̅ = 8.4,
63. Δ𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐹, if ̅̅̅̅
𝐴𝐵 = 6, ̅̅̅̅
𝐴𝐶 = 8, 𝐵𝐶
̅̅̅̅ = 5.4, what is the measure of ̅̅̅̅
𝑎𝑛𝑑 𝐷𝐹
𝐷𝐸 .
64. If b = 6 and c = 10, what is the length of a?
Classify the triangles in numbers 67 – 69 as acute, obtuse or right.
65. 6, 7, 8
66. 6, 8, 10
67. 9, 12, 17
Find the value of x and y.
68. x =
B
y
60°
7
69. y =
30°
A
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x
C
Basic Geometry Midterm Review
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Find the value of a and b.
70. a =
45°
b
71. b =
72. What is the sum of the exterior angles in a convex 12-sided polygon?
5
a
73. What is the sum of the interior angles of a 12- sided polygon?
74. What is the measure of each angle of a regular 8-sided polygon?
75. What is the distance between point R and point S?
76. Point J is located at (1,3) and point K is located (5,-3). Find the midpoint of line segment JK.
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