10th Geometry Midterm Review
Chapter 1: Essentials of Geometry
Sections 1.1 – 1.5
1.1
1.2
1.3
1.4
1.5
Points, Lines and Planes
Use segments and Congruence
Midpoint and Distance Formulas
Measure and Classify Angles
Angle Pair Relationships
Chapter 2: Reasoning and Proof
Sections 2.1, 2.2, 2.5
2.1
2.2
2.5
Inductive Reasoning
Analyze Conditional Statements
Properties from Algebra
Chapter 3: Parallel and Perpendicular Lines
Sections 3.1 – 3.6
3.1
3.2
3.3
3.4
3.5
Identify pairs of lines and angles
Use parallel lines and transversals
Prove lines parallel
Find and use slopes of lines
Write and graph equations of lines
Chapter 5 (and others): Relationships with Triangles,
Sections 4.1, 4.1, 5.1, 5.3 – 5.5
4.1
4.2
4.7
5.1
5.3
5.4
5.5
Triangle Sum Properties
Congruent Triangles
Use Isosceles and Equilateral Triangles
Mid-Segment Theorem
Perpendicular Bisectors and Angle bisectors
Medians and Altitudes
Inequalities in a Triangle
Choose the best answer for each question.
1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).
A. 13
B. 17
C. 5
D. 12
2. Points A, B and D
A. determine a plane
C. are contained in only plane P
B. are collinear
D. are noncoplanar points
F
C
A
P
E
D
B
3. What is the intersection of planes P and R.
A points A, D and B
B. AB
G
C. AB
D. AD
R
4. What is the measure of QT if R is between Q and T, QR = 14 and RT = 5?
A. 10
B. 11
C. 19
D. 9
5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).
A. (3, 4)
B. (2, 4)
C. (4, 8)
D. (1, -1)
6. What are the sides of 5 ?
A. WG and WF
B. AB and WF
C. WB and WG
D. WB and WF
E
B
1 8 9
C 2
3
4
W
5
F
6
G
A
7. 5 and 6 are
A. adjacent B. vertical
C. supplementary
D. complementary
8. 8 and 9 are
A. adjacent B. vertical
C. supplementary
D. complementary
9. 1 and 2 are
A. adjacent B. vertical
C. complementary
D. linear pair
10. 3 and 4 are
A. adjacent B. vertical
C. linear pair
D. complementary
11. Find m1 .
A. 25
C. 175
1
B. 155
D. 5
3x+10
2x+15
12. If mABD = 40 and mABC = 110 , find mDBC.
A. 150B. 130
C. 70
D. 80
D
A
B
C
7
13. Find mRSU if ST bisects RSU , m1 = 4 x − 12 and m2 = 2 x + 6.
A. 48
B. 18
C. 9
D. 24
14. Choose the converse of “If 1  2 , then m1 = m2 .
A. If m1 = m2 , then 1  2
B. If 1  2 , then 2  1
C. If m1 = m2 , then m2 = m1 .
D. None of these
R
1
T
2
U
S
15. Identify the if-then form of the following: All cars have four wheels.
a. If a vehicle has four wheels, then it is a car.
b. If a vehicle is a car, then it has four wheels.
c. If a vehicle is not a car, then it does not have four wheels.
d. None of these
16. The transitive property of equality states “If a = b and b = c, then _____ “.
A. b = a
B. a = c
C. c = b
D. b = b
20. P and Q form a linear pair and mP = 62. Find mQ.
A. 62
B. 28
C. 118
D. 90
21. Given l m and m2 = 72, find m3 . ( for 21-23, the rectangle represent parallel lines)
A. 108
B. 72
C. 18
D. 112
4
3
22. Given l m , m1 = 9x +5 and m2 = x + 37, find the value of x.
A. 32
B. 4
C. 41
D. 39
2
5
23. Given m4 = 5 x + 2 and m5 = 3x + 28, find the value of x so that l m .
A. 26
B. 13
C. 67
D. 75
l
1
m
24. A right triangle must be
A. isosceles
B. acute
C. scalene
D. either isosceles or scalene
25. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5.
A. 39
B. 13
C. 12
D. 4
26. In triangle ABC, what is the angle opposite AB ?
A. CA
B. A
C. B
D. C
27. In triangle DEF, if DE  DF and EF is the hypotenuse, then triangle DEF is
A. acute and scalene
B. right and scalene
C. right and isosceles
D. obtuse and isosceles
28. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?
A. 85
B. 95
C. 133
D. 142
29. If IGH  KLJ , then H is congruent to
A. J
B. I
C. K
D. L
C
30. Identify the median of triangle ABC.
A. CE
B. BF
C. AD
D. GH
G
F
D
31. Identify the altitude of triangle ABC.
A. CE
B BF
C. AD
D. GH
A
H
32. In triangle ABC, if mABF = 39 and BF is an angle bisector, find mBCE.
A. 90
B. 51
C. 39
D. 12
Q
33. What is the longest side of the figure QUAD.
A. DQ
B QU
C. UA
D. DA
80
46
82
D
30
A
U
E
B
34. In triangle EFG, mE = 6x – 8, mF = 7x + 3, and mG = 3x – 7. Choose the list that shows the sides
correctly ordered from shortest to longest.
A. EF , FG , EG
B. FE , EG , GF
C. EG , GF , FE
D. GF , EG , FE
35. Determine which set of numbers can be the measures of the sides of a triangle.
A. 13, 10, 16
B. 1, 2, 3
C. 5.2, 11, 4.9
D. 208, 9, 219
36. Two sides of a triangle have lengths 15 cm and 19 cm. Which measurement can be the length of the third
side?
A. 6 cm
B. 4 cm
C. 40 cm
D. 36 cm
37. If M is the midpoint of JK , m1  m2 , JL = 10x + 2, and LK = 6x + 14, which is a possible value of x?
a. 1
K
b. 2
2
c. 3
1
d. 4
J
L
38. Find the value of x.
39. Find the measure of ∠ 1.
40. Find the slope of the line that passes through A(5, 8) and B(7, 11).
41. Find the value of x when a║b.
42. Solve for x in the diagram.
43. In the diagram, WX ≅ YZ. Find the length of XZ.
44. Find the midpoint of a segment with endpoints A(-8, 5) and B(-2, 7).
45. AB bisects∠CAD. Find the value of x.
46. MQ= 30, MN = 5, MN=NO, and OP=PQ.
Find the length of OQ .