# 1. S
T
V
[A] VT
[C] VT
U
Which of the
following
best describes what
 SVT and TVU
have in common?
A
[B] VT
[D] V, T
#2.
B
C
D
E
O
A
Which of the
following is a pair
of supplementary
F
angles?
[A] BOF and BOA
[B] COD and DOE
[C] COF and AOF
[D] DOE and DOB
D
#3.
A
F
B
C
D
E Q
Which two
angles
are adjacent?
N
M
S
J
K
G
TU
H
I
C
[A] BMD and KMS
[B] MKT and NJT
[C] FJG and NJF
[D] DEQ and TIG
#4.
Plane P contains points A,
B, and C. A different plane,
plane Q, contains points B,
C, and D. Which of the
following represents the
intersection of P and Q?
B
[A] AD
[B] BC
[C] BC
[D] points B, C, A, and D
#7.
E(3, 4, - 5)
F(- 6, 10, 0)
What are the
coordinates of the
midpoint of
EF?
B
[A] (4.5, 7, 2.5)
[B] (- 1.5, 7, - 2.5)
[C] (4.5, 3, - 2.5)
[D] (- 1.5, 3, - 2.5)
#8.
What is the approximate
distance between the
points (- 13, 8) and
(206, 196) in the xy-plane?
C
[A] 219 units
[B] 269 units
[C] 289 units
[D] 299 units
Mt.
Lookout
(78,71)
Using the map, the
#9.
highway department
locates two exits between
Exit 2
Tomstown and Mount
Lookout.
From
Exit 1
Tomstown, Exit 1 is
halfway to Mount
Lookout, and Exit 2 is
Tomstown (2, 3)
three-fourths of the way
to Mount Lookout. What
are the coordinates for
Exit 2?
[A] (74, 37) [B] (59, 54)
[C] (40, 37) [D] (68, 54)
B
#10.
In the xy-plane, (-3, 1) and (4, 3)
are endpoints of a diameter of a
circle. What are the coordinates
of the center of the circle?
1
[A] ( ,2)
2
[C] (1,4)
7
[B] ( ,1)
2
7
[D] (- ,-1)
2
A
#11.
(12, 9)
(0,8)
(12, 3)
(0,2)
The county planning
department designs
a new park in the
shape of a
parallelogram. They
put in two diagonal
walkways.
What will be the coordinates of
the intersection of the diagonal
walkways?
[A] (6, 2.5)
[C] (5.5, 6)
[B] (5, 6.5)
[D] (6, 5.5)
D
#12.
3
1
2
Given: m1 = 4 x,
m 2 = (3 x + 10), and
m 3 = (2 x + 17). What is m  2?
[B] 47
[A] 61
[C] 31
[D] 17
A
#13. A
B If ABCD is a
1
rhombus and
m  ABC = 80,
what is the
measure of
 1?
C
D
[A] 40
[C] 80
A
[B] 50
[D] 90
#14.
ABCD is a parallelogram. If
m BCD = (6 x – 20) and
m DAB = (2 x + 80), what is
the value of x?
[A] 8.3
[C] 15
D
[B] 12.5
[D] 25
#15.
12 in.
N
M
Which of the
following
statements
25 in.
about the
picture is true?
O
B
[A] mO > mM
[B] mM > mN
[C] mM < mN
[D] mN < mO
#16. Write the following statement in “If-then”
B
“Two angles that form a linear pair are
form.
supplementary.”
[A] If two angles are supplementary, then they
form a linear pair.
[B] If two angles form a linear pair, then they
are supplementary.
[C]
If two angles are not supplementary, then
they form a linear pair.
[D] If two angles do not form a linear pair, then
they are supplementary.
#17. What is the inverse of the statement below?
If a triangle is scalene, then no two angles
are congruent.
[A] If the triangle is not scalene, then there are
[B]
[C]
[D]
two congruent angles.
If two angles of a triangle are congruent,
then the triangle is scalene.
If there are two congruent angles in a
triangle, then the triangle is not scalene.
If the triangle is not scalene, then there
are no congruent angles.
A
#18.
What is the contrapositive ofthe statement
below?
If a triangle is isosceles, then it has two
congruent sides.
[A]
If the triangle does not have two congruent
sides, then it is not isosceles.
[B]
If a triangle has two congruent sides, then it
is isosceles.
[C]
[D]
A
If a triangle is isosceles, then it has two
congruent sides.
A triangle has two congruent sides if and only
if it is isosceles.
#19.
The conditional statement “All 45° angles
are acute angles” is true. Based on the
conditional statement, which of the
following can be concluded from the
additional statement “The measure of  A
is 45°”?
[A]
A is an acute angle.
[B]
A is not an acute angle.
A
[C] The complement of A is not an acute
angle.
[D] The supplement of A is not an acute angle.
#20.
n
m
k
1
2
t
3
If k | | m | | n,
Which of the statements
justifies the conclusion that
1  2  3?
D
[A]
then alternate interior angles are congruent.
[B]
then vertical angles are congruent.
[C] then alternate exterior angles are congruent.
[D] then corresponding angles are congruent.
A
#21.
C
B
D
It is given that AC  AD andCAB  DAB. By the
reflexive property of congruent segments, AB  AB.
Which reason could be used to prove
Δ ABC  Δ ABD?
[A]
side-angle-side
[C]
side-side-side
A
[B]
hypotenuse-leg
[D]
angle-side-angle
#22. A
D
M
B
C
Given: ABCD is an isosceles
trapezoid. M is the midpoint
of AB.
Prove: DM  CM
#22.
M is the
midpoint of AB.
AM  MB
Def of midpoint
given
?
ABCD is an
isosceles trap.
given
ΔADM  Δ BCM
DM  CM
AD  BC
Def isos.trap.
CPCTC
#22.
[A]
What is the missing statement and
reason that completes the proof?
B
AD  BC; the legs of an isosceles
trapezoid are congruent.
 MBC; the base angles
[B] MAD
of an isos. trap. are congruent
[C] AM  BM; corresponding parts of
congruent triangles are congruent
[D]
 ABC  DAB; if lines are
parallel, s-s int.angles are supp.
#23.
X
A
Given: Δ ABC
B
Y
C
Prove: m  BAC + m  ABC + m  BCA
= 180
#23.
STATEMENTS
1) Draw XY through B and parallel
to AC.
REASONS
1) Exactly one parallel line can be
drawn to given line from pt. not on
line.
2) XBA and ABY form a linear pair. 2) Definition of a linear pair
3) m  XBA + m ABY = 180
3) The sum of the measures of the
angles of a linear pair is 180.
4) m  ABC + m CBY = m  ABY
4) Angle Addition Postulate
5) m  XBA + m ABC + m  CBY
= 180
5) Substitution
6) CBY  BCA and  XBA   BAC
6) ____________________________
7) m CBY = m BCA and
m  XBA = m  BAC
7) Definition of congruent angles
8) m  BAC + m  ABC + m  BCA
= 180
8) Substitution
#23.
[A]
[B]
What is the reason for statement 6
in the proof?
A
Alternate interior angles of
parallel lines are congruent.
Alternate exterior angles of
parallel lines are congruent.
[C] Vertical angles of parallel lines are
congruent.
[D]
Corresponding angles of parallel
lines are congruent.
#24.
What is the measure of angle y?
D
[A] 40
40°
[B] 60
x
60°
y
[C] 80
[D] 100
#25.
B
BD is the angle
bisector of ABC. If
m A = m  C = 50,
what is m  ABD?
A
D
C
[A] 30
[B] 40
[C] 45
[D] 50
B
#26.
OB bisects  AOC. If
m AOB = (3 x + 16) and
m  BOC = (8 x – 14), what
is m  AOB?
[A] 18
[C] 34
[B] 26
C
[D] 48
#27.
c
1 2
a
3 4
b
[A] Line
[B] Line
[C] Line
[D] Line
1 is supplementary to
 3 under which of the
following conditions?
A
a is parallel to line b.
a is parallel to line c.
a is perpendicular to line c.
b is perpendicular to line c.
#28.
For which type of convex polygon
is the sum of the measures of the
interior angles equal to the sum
of the measures of the exterior
angles, one at each vertex?
D
[A] triangle
[B] hexagon
[C] pentagon
[D] quadrilateral
#29.
Q
R
If m  P = 120º,
what is the sum of
the measures of
the remaining
S interior angles?
C
P 120°
[A] 240 [B] 360
U
T
[C] 600 [D] 720
#30.
The measure of each exterior
angle of a regular polygon is 45.
How many sides does the polygon
have?
[A] 4
[B] 5
[C] 8
[D] 9
C
#36.
An isosceles triangle has
vertices at (1,1) and (3, 3).
Which of the following could be
the coordinates of the third
vertex?
[A] (2, 1)
[C] (4, 1)
D
[B] (3, 2)
[D] (5, 1)
#37. Triangle MNO has vertices
with coordinates M (0, 2),
N (1, 0), and O (5, 1). What
type of triangle is Δ MNO?
[A] isosceles [B] right
[C] scalene
C
[D] equilateral
#38.
In triangle XYZ, W is
between Y and Z. The
coordinates are X (2, 3),
Y (5, 0), Z (0, 0), and
W (2, 0). What is
XW?
A
[A] altitude [B] angle bisector
[C] median [D] perpendicular
bisector of the side
#39.
What is the most specific
name for quadrilateral
ABCD with vertices A (0, 0),
B (3, 4), C (6, 0), and
D (3, - 4)?
C
[A] parallelogram
[B] rectangle
[C] rhombus
[D] trapezoid
#40.
In rectangle ABCD,
diagonal
AC = (3 x – 9) and diagonal
BD = (x + 13). What is AC?
[A] 16
[C] 24
C
[B] 18
[D] 32
#41.
In parallelogram RSTU, the
diagonals intersect at E.
If RE = 10 and
SU = 16, what is RT?
[A] 20
[B] 16
[C] 10
[D] 8
A
#42.
B
A
C
If points A, B, C,
and D form a
trapezoid, how
many ordered
pairs could
represent D?
D
[A] 1
[B] 2
[C] 3
[D] an infinite number
#43.
13
A
x-5
12
E
D
B
F
C
2x - 1
[A] 5 units
[C] 9 units
ABCD is a
trapezoid with
15 median EF.
What is the
length of AB?
A
[B] 7 units
[D] 10 units
#45.
If the sides of a triangle are
3, 7, and x, which of the
following best describes x?
[A] 4 < x < 10
[C] x < 10
[B] 4 ≤ x ≤ 10
A [D]
x>4
#46. C
X
A
Y
B
[A] 36
[B] 41
[C] 67
[D] 72
In Δ ABC, X is the midpoint of
AC and Y is the midpoint of
BC. If m  C = 67 and
m  A = 72, what is m  CYX?
B
#48.
A triangle has interior angles
that measure 3 x,
(2 x + 15), and (x + 45). What
is the measure of the largest
exterior angle?
[A] 160
[B] 125
[C] 120
[D] 115
B
#49.
B
Y
A
Z
In Δ ABC, Z is
the midpoint of
AC and Y is the
midpoint of BC.
If YZ = 21 and
C AB = (2 x – 4),
what is x?
[A] 7.25 [B] 12.5
[C] 23
[D] 46 C
#69.
Given points P (7, 5),
Q (8, 3), R (0, - 1), and
(- 1, 1), which of the following
is true?A
[A] PQ is parallel to RS.
[B] PQ is perpendicular to RS.
[C] PR is perpendicular to QS.
[D] PR is parallel to QS.
#70. Which is an equation of a line
parallel to:
2
1
- x+ y = 4
3 5
[A] - 10x + 3y = 6
[B] - 3x + 10y = 6
[C] 3x - 10y = - 6
[D] 10x + 3y = - 6
A
#71.
What is the slope of the
line that is perpendicular
to the line whose equation
is:
3x-2y=-8
3
[A]
2
2
[B]
3
2
[C] 3
3
[D] 2
C
#72.
ABCD is a rhombus.
The slope of AB is 3/8.
What is the slope of
DC?
8
[A]
3
3
[B]
8
3
[C] 8
8
[D] 3
B
#73. Which of the following is an
equation of the line
perpendicular to:
3x + 6y = 12 at (4,0)?
1
1
[B] y = x - 2
[A] y = - x + 2
2
2
[C] y = - 2x + 8
[D] y = 2x - 8
D
#74.
P
k
1
[A] y = - x
3
[C] y = - 3x - 8
Line k contains
point P and the
origin. Which is an
equation of the
line that is
perpendicular to
line k and passes
through point P?
D
1
[B] y = x + 2
3
[D] y = 3x + 10