PRACTICE MIDTERM
Geometry ~ Jan. ’14
Name _______________________________
Hour _______
PART I: Multiple Choice
1. Find the value of the variable and BC, if B is between A and C. (draw a diagram!)
1. _________
AB  5x, BC  3 x  1, AC  47
[A] 9; 27
[B] 6; 17
[C] 7; 21
[D] 6; 30
1
A
2. If AB = 53 and AC = 81, find BC.
9
cm
16
2
[A] 5 3
[B] 134
[C] 28
[D] 32
B
C
1
cm
4
3. Find the distance between the points P(5, 1) and Q(4, 2).
[A]  10
[B]
82
[C] 10
2. __________
3. __________
[D] 82
y
4. Find the length of DE.
4. __________
10
[A]
32
D
[B] 16
–10
E
[C] 32
[D]
10 x
8
–10
5. In the figure , BF bisects ABE, If mABF  8 x  15 and mFBE  10 x  1,
Find mABF .
F
E
D
A
B
C
[A] 68°
[B] 75°
[C] 71°
[D] 61°
5. __________
B
6. Name an angle complementary, but not adjacent to AOE.
[A] AOB
6.__________
C
[B] AOC
A
D
O
[C] BOC
[D] EOB
E
7. Find the unknown angle measures.
7. __________
[A] ma  40, mb  90, mc  40, md  90
[B] ma  40, mb  90, mc  50, md  90
c
40°
d
b
a
50°
[C] ma  50, mb  90, mc  50, md  90
[D] ma  50, mb  90, mc  40, md  90
8. Which shows an irregular, concave pentagon?
[A]
[B]
8.__________
[C]
[D]
̅̅̅̅, with 𝐶(−4, −3)𝑎𝑛𝑑 𝐷(6,1)
9. Find the distance from 𝐾(2,7) to the midpoint of 𝐶𝐷
[A]
9._________
3
[B] 65
[C] √65
[D] 10
10. Rewrite the statement in if-then form: All rectangles have four sides.
10. __________
[A] A figure is a rectangle if and only if it has four sides.
[B] If a figure has four sides, then it is a rectangle.
[C] A figure has four sides if and only if it is a rectangle.
[D] If a figure is a rectangle, then it has four sides.
11. Find the converse of “If it is Friday, then I go for a drive.”
11._________
[A] If it is not Friday, then I do not go for a drive.
[B] If it is Friday, then I do not go for a drive.
[C] If I do not go for a drive, then it is not Friday.
[D] If I go for a drive, then it is Friday.
12. What value of x makes the polygon regular?
12._________
[A] 11
[B] 83
[C] 3
[D] 12
13. Which of the following is false?
13._________
[A] A convex polygon can be regular.
[B] A n-gon always has n angles.
[C] A right triangle is sometimes equilateral
[D] A regular polygon is always equiangular
14. Which of the following is a valid conclusion that can be reached from (1) and (2)?
(1) If two angles form a linear pair, then they are adjacent.
(2) If two angles are adjacent, then they share no common interior points.
14. __________
[A] If two angles are adjacent, then they form a linear pair.
[B] If two angles form a linear pair, then they share no common interior points.
[C] If two angles share no common interior points, then they form a linear pair.
[D] If two angles form a linear pair, then they are congruent.
15. In the figure shown, HC || GD and mABC  113. Which of the following is false?
[A] HBF & AED are alternate exterior angles. [B] mGEF  113
[C] ABH & AEG are corresponding angles.
[D] mDEF  67
15. __________
C
D
A
E
B
H
F
G
For #16-19, use the diagram below. The lines l and m are parallel.
l
135°
7
1
16. Find the measures of 7 and 2.
16. _________
3
[A] m7  45; m2  45 [B] m7  45; m2  135
m
2
4
5
6
[C] m7  135; m2  45 [D] m7  135; m2  135
17. Identify the special name for the angle pair 1 & 2.
[A] Alternate Exterior
[B] Alternate Interior
[C] Consecutive Interior
[D] Corresponding
17. __________
18. Identify the special name for the angle pair 3 & 6.
[A] Alternate Exterior
[B] Alternate Interior
[C] Consecutive Interior
[D] Corresponding
18. ___________
19. If m4 = (5x – 10) and m1 = 135, find the value of x.
[A] 29
[B] 13
[C] 11
19. ___________
[D] 55
20. What is the measure of angle x?
20. ___________
[A] 124
[B] 146
[C] 56
[D] 112
x
34°
21. Which triangles can be proven congruent if V is the midpoint of XZ and WY ?
[A] ZVY and ZVW
[B] XVW and ZVY
[C] XVY and XVW
[D] all of these
22. Which postulate or theorem can be used to prove that ABC  DEC ?
[A] SAS
[B] ASA
[C] SSS
[D] Not enough information
23. Which postulate or theorem can be used to prove that QMN  NPQ ?
[A] SSS
[B] ASA
[C] SAS
[D] Not enough information
24. Which postulate or theorem can be used to prove that ABD  CBD ?
[A] SAS
[B] ASA
[C] SSS
[D] Not enough information
21. ___________
22. ____________
23. ___________
24. ___________
R
25. Given: RG is the angle bisector of TRI and
mTRI  8 x  12 mIRG  x  30, Find x and mTRI .
T
25. ___________
G
[A]
[B]
[C]
[D]
x  10 ; mTRI  92
x  8 ; mTRI  76
x  3 ; mTRI  36
x  5 ; mTRI  52
I
26. Find the value of x and the m2 if TU is an altitude of TVW ,
m1  8 x  52 , and m2  3x  21 .
[A]
[B]
[C]
[D]
W
T
X
26. ___________
2 1
U
x  7, m2  60
x  7, m2  30
x  11, m2  54
x  11, m2  36
V
27. Which postulate or theorem can be used to show that the triangles below are similar?
27. ___________
K
N
J
M
L
[A] SSS Similarity
[B] AA Similarity
[C] SAS Similarity
[D] The triangles are not similar.
P
28. Which postulate or theorem can be used to show that the triangles below are similar?
[A] SSS Similarity
[B] SAS Similarity
[C] AA Similarity
[D] The triangles are not similar.
29. Which postulate or theorem can be used to show that the triangles below are similar?
K
11.7
Y
J
28. ____________
29. ___________
[A] SAS Similarity
[B] AA Similarity
[C] SSS Similarity
[D] The triangles are not similar.
14.4
10
6
12
X
L
8
Z
PART II: Short Answer.
Use the figure below for problems 30 & 31.
R
Q
In the figure, QT bisects UQR and QS bisects RQT.
30. If mUQT  12a  9 and mTQR  18a  9, find a.
S
T
U
31. If mRQS  6a  4 and mTQS  7a  8, find mTQU .
32. Draw an example of vertical angles.
Mark what is true about a pair of vertical angles.
33. In the statement below, the hypothesis with one line and underline the conclusion with 2 lines.
“If I earn a 90% on my midterm, then I will get an A in Geometry”.
34. Complementary angles always have a sum of _______.
35. Explain the difference between 2 angles that form a linear pair and 2 angles that are supplementary.
Include a diagram to show how they are different.
36. List the six pairs of congruent corresponding parts if ABC  CDE. (3 angle pairs & 3 side pairs)
B
A
37. (a)
(b)
D
C
Angles: ____________
_______________
_______________
Sides: _____________
_______________
_______________
E
If a triangle has exactly 2 congruent sides it is called a(n) __________________ triangle.
If the vertex angle of this triangle is 150, what is the measure of one of the other 2 angles? ________
38. What are the next 2 numbers in the pattern? 5.25, 5.5, 5.75, _______, ________
39. Give 3 side lengths that will form a triangle and 3 side lengths that will not. Explain why and why not.
40. If the perimeter of an equilateral triangle is 90 mm, what is the length of each side? ___________
41. Draw and label an example of a regular convex polygon with 3 sides, 4 sides, and 6 sides.
42. The two triangles below are similar.
(a) Find y.
(b) Find the scale factor from the larger triangle to the smaller triangle.
12
43. Given: PQ || BC . Find x.
P
14
B
y
15
44. Which is the shortest side in the triangle?
A
10
9
15
Q
x2
C
Tell which special segment is illustrated by the diagram. (perpendicular bisector, angle bisector, median, or altitude)
45.
46.
47.
48.
___________________
_____________________
___________________
_____________________
Write a biconditional statement using the conditional statement & converse.
49.
Determine whether a true biconditional can be written from the conditional statement. If not, give a
counterexample.
50.
51.
Solve for the variable(s).
52.
54.
53.
55.
56. Find the radius of circle A, with center A(3,2) and point B(5,-2) on the circle.
A (3,2)
B (5,-2)
57. For circle A in #56, with center A(3,2) and point B(5,-2) on the circle, find the
̅̅̅̅ is a diameter of the circle.
coordinates of point C, given that 𝐶𝐵
58. A bag contains 3 blue marbles, 4, green marbles, and 5 orange marbles. You choose a marble, put it aside, and
then pick another. What is the probability that you choose 2 blue marbles?
59. A math coach is assembling a 5 player team for an upcoming tournament. If she has 14 players to choose from
how many ways can she choose a team?
60. There are 30 people in the computer club. If they are choosing a president, vice-president, and treasurer how
many ways can they do so?
61. A certain math class has 14 girls and 11 boys as shown in the table. If a student is randomly selected, find the
probability that the student is a freshman or a male.
Males
Females
Total
For 62-63 use the property to complete the statement.
62. Reflexive Property: _____  4
63. Transitive Property: Ifl  2 and 4  2, then ____  ____.
Freshmen
6
10
16
Sophomores Totals
5
11
4
14
9
25
64. Multiple Choice What type of triangle has side lengths of 14, 11, and 25?
A. Acute
B. Right
C. Obtuse
D. None
Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as
acute, right, or obtuse.
65. 26, 35, 62
66. 14, 18, 29
67. 30, 72, 78
68.
Find the value of the variable.
69. Find the value of the variable.