1. A construction engineer 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 beams are parallel?
A x=z
B y=w
C x=y
D y=z
2. What value for x will show that lines l and m are parallel?
F 25
G 30
H 40
J 60
3. A geometry student concluded:
by AAS based on the given
information A  D, C  F, and

.
Which statement can be used as a counterexample to the student’s conclusion?
A Triangles cannot be proven congruent by AAS.
B The congruent sides are not corresponding sides.
C
is an included side.
D The conclusion is valid and there is no counterexample.
4.
3Give AE and BD bisect each other at C.
Which could be used to prove
ABC  EDC ?
A (SSS) If 3 sides of one triangle are congruent to 3 sides of
another triangle, then the triangles are congruent.
B (SAS) If 2 sides and the angle between them in one triangle
are congruent to 2 sides and the angle between them in
another triangle, then the triangles are congruent.
C (ASA) If 2 angles and the side between them of one triangle
are congruent to 2 angles and the side between them of
another triangle, then the triangles are congruent.
D (AAS) If 2 angles and a side not between them are congruent
to 2 angles and a side not between them of another triangle,
then the triangles are congruent.
4.
F 26
G 59
For what measure of D is AB DC in this figure?
H 69
J 95
5. This figure represents line segments painted on a parking lot to create
parking spaces.
Which equation can be used to show that these line segments are
parallel?
A 118  x  w
C x  118  180
B 118  w  x
D w 118  180
6.
Given: In this figure, AC and BD bisect each other.
Based on the information given, which triangle congruence theorem
could be used to prove AED  CEB ?
A Angle-Angle-Side (AAS)
B Angle-Side-Angle (ASA)
C Side-Angle-Side (SAS)
D Side-Side-Side (SSS)
7.
Statement: If lines are skew, then they are not coplanar.
What is the contrapositive of the statement?
F If lines are not coplanar, then H If lines are coplanar, then they
they are skew.
are not skew.
G If lines are not skew, then
J If lines are skew, then they
they are coplanar.
are coplanar
8.
Let p  An equation is of the form y  mx  b .
Let q  Its graph is a line.
Argument: If an equation is of the form y  mx  b , then its graph is a line.
The graph is not a line.
Therefore, the equation is not of the form y  mx  b .
Which of the following is the symbolic representation of the given
argument?
A
C
B
D
9.
F
Which list has the sides of
BC, AC, AB
G AB, AC, BC
ABC ordered from longest to shortest?
H AC, AB, BC
J BC, AB, AC
10.
Three survey markers are located on a map at points H,I, and J. A triangle
is formed by connecting these markers by string so that HI = 150 feet, HJ =
245 feet, and IJ = 365 feet.
Which statement is true about the measures of the angles of
A H is the smallest
B H is the largest
HIJ ?
C I is the smallest
D I is the largest
11.
Two sides of a triangle measure 14 inches and 8 inches. Which cannot be
the length of the remaining side?
F 6 in
H 14 in
G 8 in
J 21 n
12.
This figure shows a pattern of triangles and regular hexagons.
What is the value of x ?
A 30
B 60
C 90
D 120
13.
This figure is a traffic sign in the shape of a regular octagon.
What is the value of x ?
A 45
B 60
C 135
D 180
14.
If the coordinates of A are (1,1) and the midpoint of AB is (-2,0), then the
coordinates of B are A (-0.5, 0.5)
C (-1, 0)
B (0.5, 0.5)
D (-5, -1)
15.
The figure below was formed by joining 2 segments of equal length at
common endpoint Y .
If points X , Y , and Z are non-collinear , which of the following statements
regarding XZ must always be true?
A XZ = XY
B XZ = 2(XY)
C XZ > 2(XY)
D XZ < 2(XY)
16.
RG is graphed on the coordinate grid below.
Which of the following equations best
represents the perpendicular bisector of RG ?
F
H y  3x 10
1
y  x2
3
G y  3x  8
J
1
y   x 1
3
17.
Triangles RST and VSU are shown below.
R  V , and RT  VU . Which additional condition is sufficient to prove that
RS  SV ?
F TS  SU
G VS  RU
18.
A
B
If
H RS  SU
J RS  SU
, which statement is always true?
C
D
19.
In the diagram below of
The length of
is 12 cm.
, medians
,
, and
intersect at G.
What is the length, in centimeters, of
?
F 24
H 6
G 12
J 4
20.
If two distinct planes, A and B, are perpendicular to line c, then which
statement is true?
A Planes A and B are parallel to each other.
B Planes A and B are perpendicular to each other.
C The intersection of planes A and B is a line parallel to line c.
D The intersection of planes A and B is a line perpendicular to line
c.
21.
In the diagram below, parallelogram ABCD has diagonals
intersect at point E.
Which expression is not always true?
F
H
G
J
and
that
22.
The equation of line k is
Lines k and m are
A parallel
B perpendicular
,
.
C the same line
D neither parallel nor
perpendicular
23.
Triangle ABC has vertices
classified as
F equilateral
G isosceles
24.
In
is true?
A
B
. The equation of line m is
,
, and
. The triangle may be
H right
J scalene
,
, and
. Which statement
C
D
25.
What is the slope of a line that is perpendicular to the line whose equation
is
?
A
C
B
26.
D
Which statement is logically equivalent to the given statement?
If a quadrilateral is a rhombus,then it is a parallelogram.
A If a quadrilateral is a
parallelogram, then it is a
rhombus.
B If a quadrilateral is not a
rhombus, then it is not a
parallelogram.
C If a quadrilateral is not a
rhombus, then it is a
parallelogram.
D If a quadrilateral is not a
parallelogram, then it is not a
rhombus.
27.
Given VYX is bisected by YW , mVYX  (6r 18) , and mVYW  36 . What is
the value of r ?
A 15
B 30
28.
C 36
D 72
In the figure shown, what is mZYX ?
F 36
G 77
29.
H 67
J 107
In the diagram below, PQ  MQ and mM  70 .
What is mTQP ?
A 70
B 110
C 140
D 150
30.
Which parts must be congruent to prove
Q  S and QP  SP
G Q  S
and QR  SR
F
31.
PQR  PSR by SAS?
H QRP  SRP
and QP  SP
J
QPR  SPR and QP  SP
For problems 31-33,
Given JKL  PQR . Find each value.
Find the value of x.
A 39
B 13
C 18.7
D 28.3
32.
Find the value of y.
F 1
G 13
H 9
J 25
33.
Find the value of RP .
A 25
B 19
34.
Suppose
PQR  ZYX . Which statement can you conclude?
H PQ  XY
J R   Z
PR  XZ
G P  Q
F
35.
C 1
D 17
What is the value of x ?
( 4x + 12 )
A 14
B 12
C 3
D 15
36.
What additional information do you need to prove ABC  ADC by the
SAS Postulate?
C
B
D
A
F BCA  DCA
G AB  AD
H BC  DC
J CBA  CDA
37. Label the angles and sides of each special right triangle.
45-45-90
30-60-90
SOH CAH TOA
sin 𝜃 =
cos 𝜃 =
tan 𝜃 =
38. The figure shows a person parasailing. What is x, the height of parasailer, to the nearest
foot?
39. A 24 foot tall flagpole casts a shadow 35 feet long. What is the angle of elevation of the
sun?
40. What is the approximate perimeter of ΔDEC if rectangle ABCD has a length of 4.6
centimeters?
41. Find the distance between the points (-4, 9) and (8, 1). Leave your answers in simplified
radical form. (Hint: use Pythagorean theorem)
42. Find the value of x.
43. Find the value of x and y.
44. Triangle XYZ is shown below. What is the length of segment XY in simplest radical form?
45. The elevation angle from the ground to the object to which the satellite dish is pointed is
32°. If x = 2.5 meters, how tall is the satellite stand? Round to the nearest tenth.