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Geometry Midterm Review ~ revised 12-9-15
____ 1. What is a net for the figure below?
A. C.
B. D.
____ 2. What are the names of three collinear points?
A. Points D, J, and B are collinear. C. Points A, J, and B are collinear. B. Points D, J, and K are collinear. D. Points L, J, and K are collinear.
JL
D
A
B
K
____ 3. What is the name of the ray that is opposite ?
A.
B.
C.
D.
____ 4. Which diagram shows plane PQR and plane QRS intersecting only in ?
A. C.
B. D.
____ 5. Name a fourth point in plane STZ.
A. V B. U C. Y D. S
____ 6. If , find the value of FG. The drawing is not to scale.
A. 10 C. 15
B. 12 D. 13
P
Q
R
S
E GF
____ 7. If find the values of x, EF, and FG. The drawing is not to scale.
A. x = 4, EF = 5, FG = 10 C. x = 4, EF = –5, FG = –5
B. x = 9, EF = 5, FG = 10 D. x = 9, EF = 31, FG = 44
____ 8. What segment is congruent to ?
A. B. C. D. none
____ 9. If Z is the midpoint of what are x, RZ, and RT?
A. x = 17, RZ = 53, and RT = 106 C. x = 19, RZ = 61, and RT = 122 B. x = 19, RZ = 122, and RT = 61 D. x = 21, RZ = 61, and RT = 122
____ 10. If , and , find the degree measure of
The diagram is not to scale.
A. ; C. ;
B. ; D. ;
____ 11. If then what are and The diagram is not to scale.
A. , C. ,
B. , D. ,
____ 12. Supplementary angles are two angles whose measures have a sum of ____.
Complementary angles are two angles whose measures have a sum of ____.
A. 90; 180 B. 90; 45 C. 180; 360 D. 180; 90
____ 13. and are complementary angles. m = , and m = . Find the measure of each
angle.
A. = 51, = 49 C. = 46, = 44
B. = 46, = 54 D. = 51, = 39
E GF
0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8
A EB C D
R TZ
4 61x - 15
____ 14. and are a linear pair. , and . Find the measure of each angle.
A. C.
B. D.
____ 15. bisects , , . Find . The diagram is not to scale.
A. 69 B. 96 C. 48 D. 64
____ 16. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 6) and K(6, 10).
A. (4, 8) B. (4, 4) C. (2, 2) D. (8, 16)
____ 17. M(9, 7) is the midpoint of The coordinates of S are (10, 4). What are the coordinates of R? A. (8, 10) B. (18, 14) C. (11, 1) D. (9.5, 5.5)
____ 18. Find the distance between points P(9, 4) and Q(1, 2) to the nearest tenth.
A. 68 B. 10 C. 11.7 D. 8.2
____ 19. Dan wants to put a fence around his rectangular garden. His garden measures 34 feet by 43 feet. The garden
has a path around it that is 3 feet wide. How much fencing material does Dan need to enclose the garden and
path? A. 178 ft B. 166 ft C. 89 ft D. 130 ft
____ 20. Find the circumference of the circle in terms of .
A. 2025 in. B. 180 in. C. 45 in. D. 90 in.
____ 21. If the perimeter of a square is 124 inches, what is its area?
A. 31 B. 961 C. 15,376 D. 124
____ 22. Based on the pattern, what are the next two terms of the sequence?
3, 8, 13, 18, . . .
A. 28, 33 B. 23, 28 C. 90, 450 D. 23, 450
45 in.
____ 23. Laisha’s Internet Services designs web sites and recently began a weekly advertising campaign. Laisha
noticed an increase in her customers over a period of five consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers Laisha will have in the seventh week.
A. Laisha will have 7 customers. C. Laisha will have 11 customers.
B. Laisha will have 9 customers. D. Laisha will have 13 customers.
____ 24. Write this statement as a conditional in if-then form:
All triangles have three sides.
A. If a triangle has three sides, then all triangles have three sides. B. If a figure has three sides, then it is not a triangle.
C. If a figure is a triangle, then all triangles have three sides.
D. If a figure is a triangle, then it has three sides.
____ 25. What is the converse of the following conditional?
If a number is a natural number, then it is a whole number. A. If a number is a whole number, then it is a natural number.
B. If a number is a natural number, then it is a whole number.
C. If a number is not a natural number, then it is not a whole number. D. If a number is not a whole number, then it is not a natural number.
____ 26. What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
A. If two lines do not intersect, they are parallel. One statement is false. If two lines do not
intersect, they could be skew. B. If two lines do not intersect, they are parallel. One statement is false. If two lines are
parallel, they may intersect twice.
C. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
D. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are
not parallel if (and only if) they do not intersect.
____ 27. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are congruent, then they have equal measures.
and are congruent.
A. C. =
B. + = 90 D. is the complement of .
Nu
mb
er
of
Cu
sto
mers
Week
1 2 3 4 5 6 7 8 9 10 x
1
2
3
4
5
6
7
8
9
10y
____ 28. Use the Law of Syllogism to draw a conclusion from the two given statements.
If there is a storm, then there is thunder. If there is thunder, Li's dog is under her bed.
A. There is a storm.
B. Li's dog is under her bed.
C. If there is not a storm, Li's dog is not under her bed. D. If there is a storm, then Li's dog is under her bed.
____ 29. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If an elephant weighs more than 2000 pounds, then it weighs more than Jill’s car.
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Smiley the elephant weighs 2150 pounds. A. Smiley is too heavy for the bridge.
B. Smiley weighs more than Jill’s car.
C. If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge. D. If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.
____ 30. What is the value of x? Identify the missing justifications.
, , and .
a. __________
x + 1 + x – 7 = 100 b. Substitution Property 2x – 6 = 100 c. Simplify
2x = 106 d. __________
x = 53 e. Division Property of Equality
A. Angle Addition Postulate; Addition Property of Equality
B. Angle Addition Postulate; Subtraction Property of Equality C. Protractor Postulate; Addition Property of Equality
D. Protractor Postulate; Subtraction Property of Equality
Use the given property to complete the statement.
____ 31. Transitive Property of Congruence
If ______.
A. C. B. D.
Q
P
QQ SQ
R
Drawing not to scale
____ 32. Find the values of x and y.
A. x = 18, y = 32 C. x = 32, y = 18
B. x = 64, y = 116 D. x = 116, y = 64
____ 33. What four segments are parallel to plane JKPN?
A. segments JM, KL, PQ, and NR C. segments ML, RQ, JM, and NR B. segments ML, LQ, RQ, and MR D. segments MR, LQ, NR, and PQ
Use the diagram to find the following.
J
K L
M
N
PQ
R
a
b
h
1 2
4
56
7
8 3
____ 34. Identify a pair of alternate interior angles. A. C. B. D.
____ 35. Find The diagram is not to scale.
A. 145 B. 35 C. 25 D. 45
____ 36. Which lines are parallel if ? Justify your answer.
A. , by the Converse of the Alternate Interior Angles Theorem
B. , by the Converse of the Same-Side Interior Angles Postulate
C. , by the Converse of the Alternate Interior Angles Theorem
D. , by the Converse of the Same-Side Interior Angles Postulate
____ 37. Find the value of x for which l is parallel to m. The diagram is not to scale.
A. 38 B. 141 C. 39 D. 76
____ 38. Find the values of x, y, and z. The diagram is not to scale.
A. C.
B. D.
j k
P
145°
g
h
>>
>>
>
>
l m
6
3r
s
1 2
4
5
7
8
l
m
39°
x -2 37 )º(
40°
63°
15°
x° y°z°
____ 39. Find the value of x. The diagram is not to scale.
A. 58 B. 122 C. 52 D. 160
____ 40. What is the slope of the line shown?
A.
C.
B.
D.
128°
70°
x°
(–2, 0)
(3, –6)
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
5
6
6
5
6
5
5
6
____ 41. What is the graph of ?
A.
C.
B.
D.
____ 42. Write an equation in slope-intercept form of the line through point P(–1, 2) with slope –3.
A. y – 2 = –3(x + 1) C. y – 1 = –3(x + 2) B. y = –3x – 1 D. y = –3x + 2
____ 43. Write the equation for the vertical line that contains point E(8, 7). A. x = 7 B. x = 8 C. y = 8 D. y = 7
____ 44. Write the equation for the horizontal line that contains point G(9, –3). A. x = 9 B. x = –3 C. y = –3 D. y = 9
____ 45. What is the equation in point-slope form for the line parallel to y = 5x + 10 that contains P(–3, 4)? A. y – 4 = –5(x + 3) C. x – 4 = –5(y + 3)
B. y + 4 = 5(x + 3) D. y – 4 = 5(x + 3)
____ 46. Is the line through points P(–7, –6) and Q(–6, –14) perpendicular to the line through points R(5, 0) and S(–1,
–5)? Explain.
A. Yes; their slopes are equal. B. No; their slopes are not equal.
C. Yes; their slopes have product –1.
D. No, their slopes are not opposite reciprocals.
____ 47. Are the lines y = –x – 2 and 5x – 5y = 10 perpendicular? Explain.
A. Yes; their slopes are equal.
B. No; their slopes are not opposite reciprocals. C. Yes; their slopes have product –1.
D. No; their slopes are not equal
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
____ 48. If , which of the following can you NOT conclude as being true?
A. B. C. D.
____ 49. Given and , find and
A. 5 B. 6 C. 13 D. 16
____ 50. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
A. C. B. D.
____ 51. Which triangles are congruent by ASA?
A. C. B. D. none
____ 52. Name the theorem or postulate that lets you immediately conclude
A. SAS B. AAS C. ASA D. none of these
A
B C D
( (
T
U
V
)
))
G
F
H
(
((
B
C
A
(
(
(
A
D
C
B
(
(
____ 53. Supply the missing reasons to complete the proof.
Given: and
Prove:
A. AAS; Corresp. parts of C. SAS; Corresp. parts of
B. ASA; Substitution D. ASA; Corresp. parts of
____ 54. What is the value of x?
A. 77° B. 144° C. 154° D. 72°
____ 55. Find the value of x. The diagram is not to scale.
Given: ,
A. 13 B. 15 C. 102 D. 18
N
QM
P
O
36°
Drawing not to scale
2121
xº
R UT
S
____ 56. The legs of an isosceles triangle have lengths and . The base has length . What is the
length of the base? A. 7 C. 4
B. 14 D. cannot be determined
____ 57. Find the value of x. The diagram is not to scale.
A. B. C. D. none of these
____ 58. What common side do
A. C. B. D.
____ 59. Which overlapping triangles are congruent by ASA?
A. C. B. D.
T U
(5x – 30)° (5x)°
S
R
||
A
G
E
B
D
H
C
F
____ 60. Points B, D, and F are midpoints of the sides of EC = 45 and DF = 24. Find AC.
The diagram is not to scale.
A. 45 B. 12 C. 48 D. 90
____ 61. Find the value of x.
A. 10 B. 9 C. 7 D. 12
____ 62. bisects Find FG. The diagram is not to scale.
A. 15 B. 19 C. 28 D. 14
____ 63. Where is the circumcenter of any given triangle?
A. the point of concurrency of the altitudes of the triangle
B. the point of concurrency of the perpendicular bisectors of the sides of the triangle C. the point of concurrency of the bisectors of the angles of the triangle
D. the point of concurrency of the medians of the triangle
E
C
A
D
FB
20
2x – 4
D
F
E
G
))
n + 4
2n – 6
____ 64. Find the length of , given that is a median of the triangle and AC = 44.
A. 44 C. 22
B. 88 D. not enough information
____ 65. In ACE, G is the centroid and BE = 12. Find BG and GE.
A. C.
B. BG = , GE = D. BG = , GE =
____ 66. What is the negation of this statement?
Miguel has three cats.
A. Miguel does not like cats. B. The cat has three owners.
C. Miguel does not have three cats.
D. Miguel has no cats.
____ 67. Name the smallest angle of The diagram is not to scale.
A. B. C. D. Two angles are the same size and smaller than the third.
A C
D
B
C
FA
D
E
BG
3 9 6 6
A B
C
11 9
10
____ 68. and List the sides of in order from shortest to longest.
A. B. C. D.
____ 69. Which three lengths CANNOT be the lengths of the sides of a triangle? A. 12 m, 15 m, 9 m C. 6 m, 10 m, 12 m
B. 24 m, 19 m, 12 m D. 18 m, 6 m, 11 m
____ 70. Two sides of a triangle have lengths 8 and 14. Which expression describes the length of the third side?
A. greater than 6 and at most 22 C. at least 6 and less than 22
B. greater than 6 and less than 22 D. at least 6 and at most 22
____ 71. Which of the following must be true?
The diagram is not to scale.
A. C. B. D.
____ 72. What is the range of possible values for x?
A. C. B. D.
B
C
A
34º
G
F
H
83º
S
T
R
18
10xºC
D
B(8x + 20)º
14
In the diagram, figure RQTS is the image of figure DEFC after a rigid motion.
____ 73. Name the image of C.
A. Q B. R C. F D. T
____ 74. Name the image of . A. B. C. D.
____ 75. Describe in words the translation of X represented by the translation rule .
A. 3 units to the right and 7 units down B. 7 units to the left and 3 units up
C. 3 units to the right and 7 units up
D. 3 units to the left and 7 units down
____ 76. The vertices of a triangle are P(–2, 3), Q(–4, 1), and R(8, 2). Name the vertices of .
A. C.
B. D.
____ 77. Find the image of P(–3, 2) after two reflections; first , and then .
A. (0, 0) B. (9, –6) C. (–3, 2) D. (3, –2)
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles.
____ 78. A carnival ride is drawn on a coordinate plane so that the first car is located at the point . What are the
coordinates of the first car after a rotation of 270° about the origin?
A. B. C. D.
C
D
F
E
T
S
R
S
R
Q
F
L
G
M
H
N
IP
J
Q
K
R
O
Use the figures below.
____ 79. Write a sequence of rigid motions that maps to .
A. C.
B. D.
____ 80. The dashed triangle is a dilation image of the solid triangle. What is the scale factor?
A.
B.
C.
D. 2
A
B
X
Y
P
R
T
S
D
F
E
4 8–4–8 x
4
8
–4
–8
y
8–8 x
4
8
–4
–8
y
