Name:
Block:
Date:
2015 - 2016 Geometry Mid-Year Quiz Review Packet
Due:
1/13/16 (A Day Classes)
1/14/16 (B Day Classes)
The mid-year review quiz will be on Chapters 1 through 6 that we cover in class. The BEST way to study
for the quiz will be to complete this packet, review old tests and quizzes, and look over you notes.
The review packet will be graded on:
 Completion (10 points) – On January 13th and 14th this packet will be collected in class for a
completion grade. Completion means every problem has been attempted to the best of your ability
and work has been shown. Late packets will be assessed a penalty.
 Accuracy (10 points) -- On January 20th and 21st, we will have a 10 point quiz on problems from
this packet. I will randomly select 5 problems to grade on accuracy. You will be able to use your
packet on this quiz.
Completion
10
GOOD LUCK!!!
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Chapter 1: Essentials of Geometry
1.
Use the Segment Addition Postulate to solve for p.
FE = 5p – 6
EG = 3p + 20
FG = 110
F
E
G
2.
Find the distance between A(6, 0) and B(4, 4). Keep your answer in radical form.
3.
Find the midpoint of A(6, 0) and B(4, 4).
4.
M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find the
coordinates of B.
5.
Given that mGED = 61, mGEF = 3x + 8 and mDEF = 8x – 2, find mDEF.
G
F
D
E
6.
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⃗⃗⃗⃗⃗⃗ bisects ABC. Find mABC.
In the diagram, 𝐵𝐷
7.
In the figure below, mAED = 128. Which of the following statements is false?
A]
B]
C]
D]
mBEC = 128
AEB and DEC are congruent
BEC and CED are vertical angles
mAEB = 52
D
A
E
B
C
8.
1 and 2 are supplementary angles and 1 and 3 are vertical angles. If m2 = 72, find
m3.
9.
Solve for x.
5x + 137
4x + 25
10.
Solve for x.
5x + 24
3x + 30
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For questions #11 – 13, use the diagram to the right.
11.
Name all angles that are adjacent to BOC.
B
C
A
12.
Name an angle that is complementary to COD.
O
E
13.
Name all angles that are supplementary to EOA.
14.
Which of the following statements is false?
A]
B]
C]
D]
15.
Three non-collinear points determine a plane.
Any three points lie on a distinct line.
A line contains at least two points.
Through any two distinct points there exists exactly one line.
In the figure, mCAD is twice mCAB. What is mCAB?
Chapter 2: Reasoning and Proof
16.
Rewrite the statement in if-then form: “Vertical angles are congruent.”
17.
What is the converse of the statement, “If it rains, then I carry my umbrella?”
D
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18.
What is the inverse of the statement, “If two lines are parallel, then they do not intersect?”
19.
What is the contrapositive of the statement, “If I like school, then I attend every day?”
20.
State a counter-example to the following statement: “If x2 = 25, then x = 5.”
For questions #21 – 23, decide if a conclusion can be reached. If so, write the
conclusion. If a conclusion cannot be reached, then state INVALID.
21.
If you get a hit, then your baseball team will win. You hit a home run.
22.
If it is July 4th, then we will have a picnic. If we have a picnic, then we will have fireworks.
23.
All Redskins fans are energetic. Dave is energetic.
24.
t  p
25.
p
27.
rq
26.
qs
pf
f
Let a represent “x is an odd number”. Let b represent “x is a multiple of 3”.
If x = 7, which of the following is true?
A]
ab
C]
~a  b
B]
a  ~b
D]
~a  ~b
28.
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According to the Venn diagram, which is true?
Football Players
A]
All football players play offense and defense.
B]
No football players play offense and defense.
C]
All football players play defense.
D]
Some football players play offense and defense.
Offense
Defense
Chapter 3: Parallel and Perpendicular Lines
For questions #29 – 33, line l and line m are parallel in the diagram below. Match each
statement with its correct postulate or theorem.
1
2
4
l
2 ≅ 8
A.
Alternate interior s
_____ 30.
4 ≅ 6
B.
Corresponding s
_____ 31.
2 ≅ 6
C.
Consecutive exterior s
_____ 32.
4 supp 5
D.
Consecutive interior s
_____ 33.
2 supp 7
E.
Alternate exterior s
3
5
8
34.
_____ 29.
6
m
7
Find m1, given that ⃡⃗⃗⃗⃗
𝑃𝑄 // ⃡⃗⃗⃗
𝑅𝑆.
79
P
R
1
Q
S
35.
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In the figure, l // n and r is a transversal. Which of the following is not necessarily true?
A]
2  6
B]
8  2
C]
r
1
4
7  4
D]
36.
5  3
l
6
5
8
2
3
n
7
⃡⃗⃗⃗⃗ // 𝐺𝐷
⃡⃗⃗⃗⃗ and mABC = 108. Which of the following statements is false?
In the figure shown, 𝐻𝐶
A]
mDEF = 72
B]
ABH and AEG are alternate exterior angles
C]
HBF and AED are alternate interior angles
D]
mGEF = 108
C
D
A
E
B
F
H
G
37.
Find the slope of the line passing through the points (1, 6) and (6, 5).
38.
Find the equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5.
39.
Find the equation of a line which contains the point (4, -5) and is perpendicular to the line
y = 2x + 3.
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40.
Are the following two lines parallel, perpendicular or neither?
-7x + 6y = 4 and 6x + 7y = 0
41.
Line m contains points (1, 3) and (2, 2). Which of the following pairs of points define a line
parallel to m?
42.
A]
(0, 0) and (1, 1)
B]
(0, 0) and (1, 5)
C]
(1, 1) and (6, 2)
D]
(4, 0) and (5, 5)
A construction worker needs to make sure a ceiling beam is parallel to its corresponding floor
beam. Using the drawing as a guide, which pair of measurements is sufficient to show the
beam are parallel?
A
43.
A]
x=z
B]
y=w
C]
x=y
D]
y=z
x
B
z
w
y
C
What value of x will make lines l and m parallel?
(2x + 30)
(4x – 90)
D
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44.
Using the information from the diagram, which is true?
D
C
̅̅̅̅
𝐵𝐷 // ̅̅̅̅
𝐸𝐹
A]
̅̅̅̅ // ̅̅̅̅
𝐶𝐵
𝐵𝐷
C]
45.
B]
D]
̅̅̅̅
𝐵𝐷 // ̅̅̅̅
𝐷𝐸
̅̅̅̅ // ̅̅̅̅
𝐶𝐵
𝐷𝐸
120
w
x
80
y
70
z
100
Chapter 4: Congruent Triangles
Classify NOP by its sides.
O
8
9
N
10
47.
P
Name an obtuse triangle in the diagram below.
40
60
Line l intersects lines w, x, y, and z. Which two lines are parallel?
n
46.
F
B
75
45
E
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B
35 55
65
D
30
A
49.
48.
60
The figure has angle measures as shown. What is
C mBCD?
Solve for x.
x - 10
2x
55
50.
Find the measure of ABC.
C
51
A
90
B
130
90
51.
ABC is a right triangle with right angle at C. Which are the possible measures of A and B?
Select all that apply
A]
40 and 50
B]
38 and 32
A
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52.
C]
52 and 38
D]
52 and 128
Which figures appear to be congruent?
1
3
2
4
5
53.
̅̅̅̅  ______.
If ABC  XYZ, then 𝐴𝐶
54.
If ABC  DEF, AB = 10 feet, mB = 59, and mF = 21, which of the following statements is
false?
A]
AC = DF
B]
BC = EF
C]
mD = 100
D]
B  D
In the diagram, B  E and C  F. Find the value of x.
55.
B
A
x + 50
D
75
35
C
F
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Which of the following statements must be true, if AD  BC and AB = AC?
56.
A
57.
A]
ABD  ACD by SSS
B]
ABD  ACD by SAS
C]
ABD  ACD by HL
D]
There are no congruent triangles
B
D
C
If HI = JK and IJ = LK, prove the two triangles congruent and state the method.
K
I
H
J
L
58.
Given: B  E and C  F. What other piece of information is needed to show that ABC 
DEF by ASA? Hint: Draw a diagram!
59.
Refer to the figure below. ABC  _____
D
B
C
A
E
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60.
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Which postulate or theorem can be used to prove that RST  VUT?
S
170
60
T
V
R
170
60
U
61.
Which postulate or theorem can be used to prove that ABC  EDC?
A
C
B
D
E
62.
̅̅̅̅ and ̅̅̅̅
Given that ̅̅̅̅
𝐴𝐷 ≅ 𝐵𝐶
𝐴𝐶 ≅ ̅̅̅̅
𝐵𝐷, which postulate or theorem could be used to prove that
DCA  CDB?
A
D
63.
B
C
Find the value of x and y.
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64.
Find the values of x and y.
x
110
65.
y
̅̅̅̅ ≅ 𝐶𝐵
̅̅̅̅, which term does not describe the triangle?
In ABC, 𝐴𝐵
B
A]
B]
C]
D]
Equilateral
Isosceles
Acute
Obtuse
3x - 2
C
x+4
7
A
Chapter 6: Similarity
66.
Solve for a:
10
5

a2 a2
67.
At the same time of day, a man who is 75 inches tall casts a 52.5-inch shadow and his son casts
a 35-inch shadow. Determine the height of the man’s son.
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For questions #68 – 70, identify the similarity postulate or theorem used to prove that
∆ABC  ∆XYZ. Sketch pictures if necessary. Also, state the scale factor, if possible.
68.
The side lengths of ABC are 3, 4, 6, and the side lengths of XYZ are 9, 12, 18.
69.
In ABC, mA = 15 and mB = 80. In XYZ, mY = 80 and mZ = 85.
70.
In ABC, mB = 60 and AB = 6, and BC = 12. In XYZ, mY = 60 and XY = 12, and YZ =
24.
For question #70 use the diagram to the right. Round to the nearest tenth.
70.
a)Length of GB.
b) Length of FC.
c) Length of BC.
d) Length of CD.
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Chapter 5: Triangle Inequality
71.
The longest side in the figure is
.
N
70
L
105 P
65
30
M
72.
Two sides of a triangle have lengths 12 and 27. The length of the third side must be greater
than _____ and less then _____.
73.
On the shores of a river, surveyors marked locations A, B, and C. mACB = 70 and mABC =
65. List the distances between these locations in order, least to greatest?
74.
Which of the following could be the sides of ABC?
75.
A]
AB = 12, BC = 15 and AC = 2
B]
AB = 9, BC = 15, AC = 4
C]
AB = 150, BC = 100, AC = 50
D]
AB = 10, BC = 8, AC = 12
Three lookout towers are located at points A, B, and C on a section of the national forest shown
in the diagram. Which of the following is true concerning ABC formed by the towers?
A]
mA is greatest
B]
mC is greatest
C
4123 km
C]
D]
5385 km
mA is least
mC is least
A
B
4472 km