GEOMETRY
2015 Midterm Review
Name: ___________________________
Period: ____
Date: ___________
To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the
following chapters. Use this guide to help you practice.
Chapter 1 (1.1 – 1.4):
Points Lines and Planes
Segments and Congruence
Midpoint and Distance Formulas
Measure and Classify Angles
Describe Angle Pair Relationships
Chapter 2:
Conditional Statements (Converse, Inverse, Contrapositive, Biconditional)
Postulates and Diagrams
Reasoning Properties from Algebra
Proving Geometric Statements
Chapter 3 (3.1 – 3.6):
Parallel Lines and Angle Relationships (Corresponding, Consecutive, Alternate Interior/Exterior)
Perpendicular Lines
Find and Use Slopes of Lines
Write and Graph Equations of Lines
Chapter 4 (4.1 – 4.7):
Triangle Classification (Acute, Obtuse, Right, Equiangular, Equilateral, Scalene, Isosceles)
Triangle Sum Properties
Triangle Congruence (SSS, SAS, AAS, ASA, HL)
Isosceles and Equilateral Triangle Properties
Chapter 5 (5.5 – 5.6):
Inequalities in a Triangle
Relationships Between Side Lengths and Angle Measures
Inequalities in Two Triangles (Hinge Theorem)
Chapter 6:
Ratios, Proportions, Geometric Mean
Prove Triangles are Similar (AA, SSS, SAS)
Use Proportionality Theorems
Geometry
Midterm Review
Name: ___________________________
Period: ____
Date: ___________
1) Ray PR is shown in which sketch?
a)
b)
c)
P
Q
R
d)
R
P
P
Q
R
Q
Q
R
P
2) If RS = 32.2 and QS = 62.8, find QR.
R
Q
S
3) Use the Segment Addition Postulate to solve for p.
FE = 4p + 20
F
EG = 5p + 16
E
G
FG = 45
a) p = 1
b) p = 4
c) p = 5
d) p = 6
4) Find the distance between A(6, 0) and B(4, 4).
a) 116
b) 2 5
c)
116
d) 20
5) Find the midpoint of A(6, 0) and B(4, 4).
6) M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find the
coordinates of B.
7) Which of the following angles measures 125?
a)
b)
c)
d)
8) If mJOL = 50 and mKOL = 27, then what is the measure of JOK?
a) 25
b) 23
c) 28
d) 20
J
K
O
L
9) Given that mGED=60, mGEF=2x + 7 and mDEF=7x – 1, find mGEF and mDEF.
G
F
E
D
10) In the figure below, mAED = 128. Which of the following statements is false?
a)
b)
c)
d)
E
B
11) 1 and 2 are ______.
a)
b)
c)
d)
1
a linear pair
complementary angles
supplementary angles
vertical angles
2
12) Find the measure of 1.
a)
b)
c)
d)
42
48
58
138
42
1
13) Solve for x.
5x + 137
4x + 25
14) Solve for x.
5x + 24
3x + 30
15) Name an angle that is adjacent to BOC
a)
b)
c)
d)
DOE
AOE
DOB
BOA
D
A
mBEC = 128
AEB and DEC are congruent
BEC and CED are vertical angles
mAEB = 52
B
C
A
O
E
D
C
16) Using the diagram, name an angle that is complementary to COD.
a) AOE
b) BOC
c) DOE
B
d) AOC
C
A
O
17) Rewrite the statement in if-then form: Vertical angles are congruent.
E
18) What is the converse of the statement, “If it rains then I carry my umbrella.”?
a)
b)
c)
d)
“If it does not rain, then I do not carry my umbrella.”
“If I do not carry my umbrella, then it does not rain.”
“If I do not carry my umbrella, then I will get wet.”
“If I carry my umbrella, then it rains.”
19) “If I get a chance then I will succeed.” In this conditional statement, the underlined portion is
called the __________________________.
20) What is the inverse of the statement, “If two lines are parallel, then they do not intersect.”?
a)
b)
c)
d)
“If two lines are not parallel then they intersect.’
“If two lines intersect then they are not parallel.”
“If two lines do not intersect then they may be skew.”
“If two lines do not intersect then they are not parallel.”
21) Which of the following statements is false?
a)
b)
c)
d)
Three non-collinear points determine a plane.
Any three points are collinear.
A line contains at least two points.
Through any two distinct points there exists exactly one line.
22) Rewrite the biconditional statement as a conditional statement and its converse.
Biconditional: “I am lactose intolerant if and only if I am allergic to milk products”
Conditional:
Converse:
23) Write the converse of the conditional statement and decide if the statement can be written as a
biconditional.
If I got a speeding ticket, then I was exceeding the speed limit.
Converse:
Biconditional?
D
24) State a counterexample to the following statement:
a)
b)
c)
d)
“If x2 = 25, then x = 5.”
x=5
x = 5
x2 = 25
x 2 = 100
25) The figure at right represents which of the following statements?
C
a)
b)
c)
d)
two perpendicular rays
two perpendicular lines
a straight angle
AB = AC
A
B
26) Define each of the following terms.
- Deductive reasoning
- Inductive reasoning
27) Provide an example of each of the following:
- Law of Syllogism
- Law of Detachment
B
28) In the cube shown at right, AD and HG are called _____
a)
b)
c)
d)
A
parallel lines
perpendicular lines
intersecting lines
skew lines
D
F
H
n
2
same-side interior angles
corresponding angles
alternate interior angles
alternate exterior angles
corresponding angles
alternate interior angles
alternate exterior angles
consecutive interior angles
l
m
1
30) In the figure, 6 and 3 are _____
A)
B)
C)
D)
G
E
29) In the figure shown, 1 and 2 are ____
a)
b)
c)
d)
C
n
1
4
5
8
2
l
3
6
m
7
31) In the figure above, 6 and 2 are ____________________________________ angles.
79
P
32) Find m1, given that PQ || RS
a) 11
b) 79
c) 91
R
1
d) 101
33) Complete the following 2-column proof:
Given: JM  LM & mKJM  mKLM  90
Prove: JK  KL
Given
Given
34) Write a proof of the following:
Given: AB ED & AB  ED
Prove: ABC  DEC
Given
35) Write a proof of the following:
Given: IH  HK & IJ  JK
Prove: IHJ  KHJ
Given
36) Complete the following statements:
If
c 2  a 2  b 2 , then the triangle is a _____________ triangle.
c 2  a 2  b 2 , then the triangle is an _____________ triangle.
2
2
2
If c  a  b , then the triangle is an _____________ triangle.
If
Q
S
37) In the figure, l n and r is a transversal.
r
Which of the following is not necessarily true?
a)
b)
c)
d)
2  6
8  2
7  4
5  3
1
2
4
6
5
8
l
3
n
7
38) In the figure shown, HC GD , and mABC = 108.
Which of the following statements is false?
a)
b)
c)
d)
C
D
mDEF = 72
ABH and AEG are alternate exterior angles
HBF and AED are alternate interior angles
mGEF = 108
A
E
B
F
H
G
39) Find the slope of the line passing through the points (1, 6) and (6, 5).
y
40) A line parallel to
a) y  
2
x7
3
2
x  7 is:
3
b) y  
3
x7
2
c) y 
3
x2
2
d) y 
2
x 1
3
41) Which describes the relationship between the lines with equations
 7 x  6 y  4 and 6 x  7 y  0 ?
a) parallel
b) same line
c) perpendicular
d) neither parallel nor perpendicular
O
42) Classify NOP.
a) Equilateral
8
9
b) Isosceles
c) Scalene
d) none of these
N
10
P
B
43) Name an obtuse triangle in the diagram at right.
35 55
65
D
30
A
44) Find the value of x.
a) 80
b) 100
x
c) 160
d) 170
10
60
C
45) Solve for x.
2x
x - 10
55
46) Which figures appear to be congruent?
a)
b)
c)
d)
1
3 and 4
1, 2, and 4
2 and 5
1 and 4
3
2
4
5
47) If ABC  XYZ, then AC  ______.
48) If JKL  STU, JK = 10 feet, mK = 59, and mU = 21, which of the following is false?
a) JL = SU
b) KL = TU
d) K  S
c) mS = 100
B
49) In the diagram, B  E and C  F. Find the value of x.
A
x + 50
D
75
35
C
F
E
B
50) What must be true for ABC  EDC by SAS?
a) B  D
c) AC  CE
E
b) AB  DE
d) A  E
C
A
D
51) Which of the following statements must be true, if AD  BC and AB = AC?
a)
b)
c)
d)
A
ABD  ACD by SSS
ABD  ACD by SAS
ABD  ACD by HL
There are no congruent triangles
B
a) EDC
c) ACE
D
B
52) Refer to the figure at right. ABC  _____
C
b) EDA
d) CDE
A
E
D
C
A
53) Using just the information shown in the diagram, which postulate
or theorem can be used to prove that ABC  EDC?
C
D
B
E
54) What is the measure of each base angle of an isosceles triangle if its vertex angle measures 32
and its 2 congruent sides measure 17 inches?
55) In ABC, if AB  BC and mA = 39, then mC = ______.
a) 39
b) 51
c) 102
d) 141
56) Find the values of x and y.
a) x = 70 and y = 50
c) x = 40 and y = 70
x
b) x = 40 and y = 110
d) x = 70 and y = 110
110
y
A
57) Identify the longest side of the triangle.
65
B 60
55
C
P
58) Arrange the angles of the triangle in order, from largest to smallest.
a) P, Q, R
c) Q, R, P
25
20
b) P, R, Q
d) Q, P, R
Q
22
N
59) The longest side in the figure is _______
a)
b)
c)
d)
NM
70
L
105 P
ML
LN
MP
65
30
M
60) Two sides of a triangle have lengths 12 and 27.
The length of the third side must be greater than _____ and less then _____.
a) 14, 40
b) 15, 39
c) 11, 28
d) 12, 27
R
61) Which side lengths allow you to construct a triangle?
a) 7, 2, and 2
b) 2, 3, and 8
c) 1, 4, and 9
d) 6, 8, and 10
62) Which Geometric concept do you think you could use later in life? Give an example.
63) In the figure shown, mAED = 110. Which statement is false?
a)
b)
c)
d)
A
mAEB = 80
AEB and DEC are vertical angles
BEC and CED are adjacent angles
mBEC = 110
64) If line a is parallel to line b, what is m1?
D
E
B
C
1
a
b
40
65) Lines AB and CD intersect at P. PR is
perpendicular to AB and mAPD = 170.
What is the measure of DPB?
a)
b)
c)
d)
10
20
30
40
66) A ladder is leaning against a house at an angle of 38, as shown in the diagram.
What is the measure of the angle x, that the ladder makes with the ground?
67) Line a is parallel to line b if:
a) m4 = m2
c) m4 = m5
2
1
b) m3 = m5
d) m3 = m2
3
a
4
5
6
7
8
b
68) ABC is a right triangle with right angle at C. Which are the possible measures of A and B?
a)
b)
c)
d)
48 and 50
38 and 32
52 and 38
52 and 128
69) Which conclusion follows logically from the true statements?
“If negotiations fail, then the baseball strike will not end.”
“If the baseball strike does not end, then the World Series will not be played.”
a)
b)
c)
d)
If the baseball strike ends, the World Series will be played.
If negotiations do not fail, the baseball strike will end.
If negotiations fail, the World Series will not be played.
If negotiations fail, the World Series will be played.
70) Given that AD  BC and AC  BD , which could be used to prove that DCA  CDB?
a) SSS
c) ASA
b) SAS
d) AAS
71) On the shores of a river, surveyors marked locations A, B, and C. mACB = 70 and
mABC = 65. Which lists the distances between these locations in order, least to greatest?
B
C
A
72) The figure has angle measures as shown. What is mBCD?
73) What is m3?
a) 65
c) 85
b) 75
d) 90
3
65
150
74) Which of the following could be the lengths of the sides of ABC?
a)
b)
c)
d)
AB = 12, BC = 15, AC = 2
AB = 9, BC = 15, CA = 4
AB = 150, BC = 100, CA = 50
AB = 10, BC = 8, AC = 12
75) To find the contrapositive of a conditional statement you should:
a)
b)
c)
d)
Find the inverse of the converse of the original statement.
Find the converse of the inverse of the original statement.
Negate the hypothesis and conclusion of the converse of the original statement.
All of the above.
76) 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)
b)
c)
d)
mA is greatest
mC is greatest
mA is least
mC is least
C
4123 km
5385 km
B
A
4472 km
77) What value of x will make lines l and m parallel?
2x + 30
4x - 90
C
78) In the figure, mCAD is twice mCAB. What is mCAB?
a)
b)
c)
d)
120
60
45
30
D
A
B
79) Triangle XYZ is a right triangle with the right angle at Z.
Which are possible measures for angle X and angle Y?
a) 40 and 42
c) 48 and 50
b) 44 and 46
d) 52 and 54
80) Explain the difference between similar triangles and congruent triangles. Be specific.
Questions 81-94: True/False.
81) It is possible to have a triangle with side lengths 7, 7, and 9.
a) True
b) False
82) Corresponding parts of congruent triangles are equal in measure.
a) True
b) False
83) Coplanar points are collinear.
a) True
b) False
84) Collinear points are coplanar.
a) True
b) False
85) SSA is a method to prove triangle congruency.
a) True
b) False
86) When two planes intersect, they form a line.
a) True
b) False
87) Equilateral triangles are equiangular.
a) True
b) False
88) Skew lines are coplanar.
a) True
b) False
89) If two lines are parallel, they have the same slope.
a) True
b) False
90) A right triangle can have up to two right angles.
a) True
b) False
91) In a right triangle, the hypotenuse is adjacent to the right angle.
a) True
b) False
92) The slope of a horizontal line is zero.
a) True
b) False
93) The AAA method is used to prove that triangles are congruent.
a) True
b) False
94) A scalene triangle never has congruent sides.
a) True
b) False
Complete the following sentences with always, sometimes, or never.
95)
96)
97)
98)
An isosceles triangle is _____________________ a right triangle.
An obtuse triangle is _____________________ a right triangle.
A right triangle is _____________________ an equilateral triangle.
A right triangle is _____________________an isosceles triangle.
8 in
2 ft
99) Simplify the following ratio as much as possible:
a)
4
1
100) Solve the proportion:
b)
x2 1

10
2
4 in
1 ft
c)
8
24
d)
1
3
101) In the diagram ABC ~ XYZ. Find YZ.
a) 9/2
b) 2
c) 5
d) 8
102) Let p represent “Line AB and line BC are perpendicular” and let q represent “ABC is a right
angle”. Which represents the contrapositive of “If line AB and line BC are perpendicular, then
ABC is a right angle”?
a) q →
b) q →
c) ~q →
d) ~q →
p
~p
p
~p
103) Are the two triangles in this diagram similar? If so, give the similarity statement.
a)
b)
c)
d)
Yes, ABC ~ CDE
Yes, ABD ~ EDC
Yes, ABD ~ ECD
No, the triangles are not similar.
104) In the diagram shown on the right, what is the length of AB ?
a) 4
b) 3/2
c) 8/3
d) 16
105) If two sides of a triangle have lengths 7 and 11, which is a possible length for the third side of
the triangle?
a)
b)
c)
d)
18
5
4
2
106) The coordinates of the midpoint of line segment CD are (4, -5) and the coordinates of C are
(8, -8). What are the coordinates of D?
107) If two triangles have one pair of congruent angles and if the lengths of the corresponding
adjacent sides are proportional, then the triangles are:
a) equal
b) congruent
c) similar
d) obtuse
108) The ratio of the volumes of two similar rectangular prisms is 64:125. What is the ratio of their
surface areas?