Name:
Geometry
Date:
Block:
2013 – 2014 Geometry Midterm Review Packet
Due:
1/9/14
1/10/14
(A Day Classes)
(B Day Classes)
The midterm will be on Chapters 1 through 4, Chapter 6 and material from Chapter 7 that we cover in
class. The BEST way to study for the midterm will be to look over all past tests and quizzes because
the following review packet covers most, but not all, topics covered! It will be graded and is worth a
total of 40 points. This must be done in pencil; no pen!!
The midterm review will be graded on:
 Completion (20 points) – On January 9th and 10th 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 (20 points) – The problems are worked out and solved correctly. I will randomly
select problems to grade for accurate work. This packet is due on exam day for accuracy
points.
Completion
Accuracy
20
20
GOOD LUCK!!!
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Chapter 1: Essentials of Geometry
For questions #1 – 5, match the symbolic notation with its correct meaning.
1.
⃡𝐴𝐵
A.
line segment AB
2.
𝐴𝐵
B.
distance of AB
3.
̅̅̅̅
𝐴𝐵
C.
ray AB
4.
𝐴𝐵
D.
congruent to
5.
≅
E.
line AB
6.
If RS = 46.2 and QS = 83.7, find QR.
Q
7.
R
S
Use the Segment Addition Postulate to solve for p.
FE = 5p – 6
EG = 3p + 20
FG = 110
F
E
G
8.
Find the distance between A(6, 0) and B(4, 4). Keep your answer in radical form.
9.
Find the midpoint of A(6, 0) and B(4, 4).
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10.
M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find the
coordinates of B.
11.
Which of the following angles measures 125?
12.
A]
B]
C]
D]
If mJOL = 60 and mKOL = 37, then what is the measure of JOK?
J
K
O
L
13.
Given that mGED = 61, mGEF = 3x + 8 and mDEF = 8x – 2, find mDEF.
G
F
D
E
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14.
In the diagram, 𝐵𝐷 bisects ABC. Find mABC.
15.
In the figure below, mAED = 128. Which of the following statements is false?
A]
mBEC = 128
B]
AEB and DEC are congruent
C]
BEC and CED are vertical angles
D]
mAEB = 52
D
A
E
B
C
16.
A
of angles is formed when the non-shared sides of two
adjacent angles form a pair of opposite rays.
17.
1 and 2 are what type of angles?
1
2
18.
1 and 2 are supplementary angles and 1 and 3 are vertical angles. If m2 = 72, find
m3.
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19.
Solve for x.
5x + 137
4x + 25
20.
Solve for x.
5x + 24
3x + 30
For questions #21 – 23, use the diagram to the right.
21.
Name all angles that are adjacent to BOC.
B
C
22.
Name an angle that is complementary to COD.
A
O
D
E
23.
Name all angles that are supplementary to EOA.
24.
The figure to the right represents which of the following statements?
A]
two perpendicular rays
B]
two perpendicular lines
C]
a straight angle
D]
AB = AC
C
A
B
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25.
26.
Which of the following statements is false?
A]
Three non-collinear points determine a plane.
B]
Any three points lie on a distinct line.
C]
A line contains at least two points.
D]
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
27.
Rewrite the statement in if-then form: “Vertical angles are congruent.”
28.
What is the converse of the statement, “If it rains, then I carry my umbrella?”
29.
What is the inverse of the statement, “If two lines are parallel, then they do not intersect?”
30.
What is the contrapositive of the statement, “If I like school, then I attend every day?”
31.
“If I get a chance, then I will succeed.” In this conditional statement, the underlined portion is
called what? The double underlined portion is called what?
Underlined =
32.
Double underlined =
State a counter-example to the following statement: “If x2 = 25, then x = 5.”
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For questions #33 – 38, decide if a conclusion can be reached. If so, write the
conclusion. If a conclusion cannot be reached, then state INVALID.
33.
If you get a hit, then your baseball team will win. You hit a home run.
34.
If it is July 4th, then we will have a picnic. If we have a picnic, then we will have fireworks.
35.
All Redskins fans are energetic. Dave is energetic.
36.
t  p
p
39.
Let a represent “x is an odd number”.
Let b represent “x is a multiple of 3”.
37.
rq
qs
38.
pf
f
If x = 7, which of the following is true? (The  symbol means “and”)
40.
A]
ab
B]
a  ~b
C]
~a  b
D]
~a  ~b
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
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Chapter 3: Parallel and Perpendicular Lines
For questions #41 – 43, use the diagram below to state whether the following lines are
parallel, perpendicular or skew.
C
B
A
D
G
F
H
41.
⃡𝐶𝐷 and ⃡𝐹𝐸 are
42.
⃡𝐺𝐹 and ⃡𝐺𝐻 are
43.
⃡ and 𝐻𝐸
⃡ are
𝐴𝐵
E
For questions #44 – 48, 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
_____ 45.
4 ≅ 6
B.
Corresponding s
_____ 46.
2 ≅ 6
C.
Consecutive exterior s
_____ 47.
4 supp 5
D.
Consecutive interior s
_____ 48.
2 supp 7
E.
Alternate exterior s
3
5
8
49.
_____ 44.
6
m
7
Find m1, given that ⃡𝑃𝑄 // ⃡𝑅𝑆.
79
P
R
1
Q
S
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50.
51.
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]
7  4
D]
5  3
r
1
4
l
6
5
8
2
3
n
7
In the figure shown, ⃡𝐻𝐶 // ⃡𝐺𝐷 and mABC = 108. Which of the following statements is false?
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
52.
Find the slope of the line passing through the points (1, 6) and (6, 5).
53.
Find the equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5.
54.
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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55.
Are the following two lines parallel, perpendicular or neither?
-7x + 6y = 4 and 6x + 7y = 0
56.
57.
Line m contains points (1, 3) and (2, 2). Which of the following pairs of points define a line
parallel to m?
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
A]
B
x=z
x
B]
y=w
C]
x=y
z
w
y
D]
y=z
C
58.
What value of x will make lines l and m parallel?
(2x + 30)
(4x – 90)
D
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59.
If line a is parallel to line b, what is m1?
a
1
b
56
60.
This diagram shows how a periscope works. If the two mirrors are parallel and m1 = m3,
what is m6 when m2 = m5 = 90?
61.
Using the information from the diagram, which is true?
D
C
A]
̅̅̅̅
𝐵𝐷 // ̅̅̅̅
𝐸𝐹
B]
̅̅̅̅
𝐵𝐷 // ̅̅̅̅
𝐷𝐸
C]
̅̅̅̅ // ̅̅̅̅
𝐶𝐵
𝐵𝐷
D]
̅̅̅̅ // ̅̅̅̅
𝐶𝐵
𝐷𝐸
F
40
60
B
62.
Line l intersects lines w, x, y, and z. Which two lines are parallel?
n
120
w
x
80
y
70
z
100
75
45
E
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Chapter 4: Congruent Triangles
Classify NOP by its sides.
63.
O
8
9
N
10
64.
P
Name an obtuse triangle in the diagram below.
B
35 55
30
A
65.
65
D
60
C
A triangle has angle measures of 60, 60, and 60. Classify the triangle by its angles and sides
by the most specific name.
Angles =
Sides =
66.
How many obtuse angles can a triangle have?
67.
The figure has angle measures as shown. What is mBCD?
68.
What is m3?
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69.
Solve for x.
x - 10
2x
55
70.
Find the measure of ABC.
C
51
A
90
B
130
71.
72.
ABC is a right triangle with right angle at C. Which are the possible measures of A and B?
A]
48 and 50
B]
38 and 32
C]
52 and 38
D]
52 and 128
A
C
Which figures appear to be congruent?
1
3
2
4
73.
90
5
̅̅̅̅  ______.
If ABC  XYZ, then 𝐴𝐶
B
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If ABC  DEF, AB = 10 feet, mB = 59, and mF = 21, which of the following statements is
false?
74.
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.
75.
B
A
x + 50
D
75
35
C
F
E
Which of the following statements must be true, if AD  BC and AB = AC?
76.
A
77.
A]
ABD  ACD by SSS
B]
ABD  ACD by SAS
C]
ABD  ACD by HL
D]
There are no congruent triangles
B
D
If HI = JK and IJ = LK, prove the two triangles congruent and state the method.
K
I
H
J
L
C
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78.
Given: B  E and C  F. What other piece of information is needed to show that ABC 
DEF by ASA? Hint: Draw a diagram!
79.
Refer to the figure below. ABC  _____
D
B
C
A
80.
E
Which postulate or theorem can be used to prove that RST  VUT?
S
170
60
T
V
R
170
60
U
81.
Which postulate or theorem can be used to prove that ABC  EDC?
A
C
B
D
E
82.
̅̅̅̅ and ̅̅̅̅
Given that ̅̅̅̅
𝐴𝐷 ≅ 𝐵𝐶
𝐴𝐶 ≅ ̅̅̅̅
𝐵𝐷, which postulate or theorem could be used to prove that
DCA  CDB?
A
D
B
C
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83.
Find the value of x and y.
84.
Find the values of x and y.
x
110
85.
y
̅̅̅̅, which term does not describe the triangle?
In ABC, ̅̅̅̅
𝐴𝐵 ≅ 𝐶𝐵
A]
Equilateral
B]
Isosceles
C]
Acute
B
3x - 2
C
D]
Obtuse
x+4
7
A
*DON’T FORGET TO REVIEW YOUR CONGRUENT TRIANGLES PROOFS TOOLBOX!!*
Chapter 6: Similarity
86.
Solve for a:
10
5

a2 a2
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87.
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.
For questions #88 – 90, identify the similarity postulate or theorem used to prove that
∆ABC  ∆XYZ. Sketch pictures if necessary. Also, state the scale factor for 88 and 90.
88.
The side lengths of ABC are 3, 4, 6, and the side lengths of XYZ are 9, 12, 18.
89.
In ABC, mA = 15 and mB = 80. In XYZ, mY = 80 and mZ = 85.
90.
In ABC, mB = 60 and AB = 6, and BC = 12. In XYZ, mY = 60 and XY = 12, and YZ =
24.
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For questions #91 – 94, use the diagram to the right. Round to the nearest tenth.
91.
Length of GB.
92.
Length of FC.
93.
Length of BC.
94.
Length of CD.
Chapter 7: Right Triangles and Trigonometry
95.
Simplify the following radicals:
A]
96.
√150
B]
√63
An airplane is 34 ground miles from the end of the runway (GA) and 6 miles high (PG) when it
begins its approach to the airport. To the nearest mile, what is the distance (PA) from the
airplane to the end of the runway?
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97.
̅̅̅̅ .
Triangle ABC is a right triangle with the measures shown. Find the length of 𝐵𝐶
98.
Arrange the angles of the triangle in order, from largest to smallest.
P
25
20
Q
99.
22
R
The longest side in the figure is
.
N
70
L
105 P
65
30
M
100.
Two sides of a triangle have lengths 12 and 27. The length of the third side must be greater
than _____ and less then _____.
101.
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?
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102.
103.
Which of the following could be the sides of ABC?
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]
104.
5385 km
mA is least
A
mC is least
B
4472 km
Decide whether the numbers can represent the side lengths of a triangle. If they can, classify
the triangle as acute, right, or obtuse.
A]
3, 4, 6
B]
8, 10, 12
C]
5, 9, 14
D]
5, 12, 13