Geometry
CRCT Review Problems
#1

There are two rectangles, ABCD and WXYZ. The
measure of each side of WYXZ is 5 times the
measure of each corresponding side of ABCD.
Which statement is true of the areas of these two
rectangles?
A. The area of WXYZ is 5 times the area of ABCD
B. The area of WXYZ is 10 times the area of ABCD
C. The area of WXYZ is 20 times the area of ABCD
D. The area of WXYZ is 25 times the area of ABCD
#2

If two lines lie in the same plane and do
NOT intersect, they are called _______.
A. bisectors
B. horizontal
C. parallel
D. perpendicular
#3

If ABC
is reflected
across the x-axis,
what are the resulting
coordinates of point
B?
A. (3, 1)
B. (-3, 1)
C. (-3, -1)
D. (3, -1)
#4

A model of a house has been drawn on a
coordinate grid. One corner of the house
has been drawn at (1, 5). The drawing will
be translated two units up and three units
to the right. Where will the same corner of
the house be after the translation?
A. (-2, 3)
B. (-1, 2)
C. (3, 8)
D. (4, 7)
#5

A point was graphed at (-3, 3). The point
was translated to (3, 3) and then translated
to (3, -3). Which translations occurred.
A. two equal dilations
B. reflection over the x-axis, then a rotation
C. reflection over the y-axis, then a reflection
over the x-axis.
D. reflection over the x-axis, then a reflection
over the y-axis
#6

Susan has two boxes. Each box is 12 cm
high, 12 cm long, and 12 cm wide. Which
statement describes Susan’s boxes?
A. The boxes are congruent, but not similar
B. The boxes are similar, but not congruent
C. The boxes are similar and congruent
D. The boxes are only similar
#7

Suppose a cone is cut by a plane. Which
cross-section is NOT possible?
A. circle
B. ellipse
C. square
D. triangle
#8

The triangles shown are congruent. Which two
sides MUST be proportional?
A. CM and SV
B. CM and MT
C. CT and VU
D. CT and MT
#9

In the diagram JKL ~ MNO. Find scale
factor (small to large) of the two triangles.
A. 2:5
B. 2:3
C. 3:2
D. 5:2
#10
FHJ ~ YCL.Which of the following is a pair
of corresponding angles?
A. F and J
B. H and Y
C. C and J
D. Y and F
#11

The triangles are
similar. Which
statement shown is a
correct similarity
statement?
A. BCA ~ EDF
B. BAC ~ EDF
C. CBA ~ DFE
D. CBA ~ FDE
#12

Given: ABC ~ DEF Side AB = 1.5 units.
Side ED = 3.75 units. Side BC = 3 units.
What is the length of side EF?
A. 2.25 units
B. 2.5 units
C. 7.5 units
D. 11.25 units
#13

For the construction
shown, which of the
following arcs must
be drawn first?
A. 1
B. 2
C. 3
D. 4
#14
The diagram shows a
geometric figure on a
coordinate plane.
 Which diagram shows a rotation of the
geometric figure?

#15

What must the vale of x be in order for
the figures below to be similar?
A. 16 cm
C. 12 cm
B. 14 cm
D. 10 cm
#16

What three-dimensional figure will be
formed if the right triangle shown is
rotated about the line shown?
A. cone
B. cylinder
C. cube
D. sphere
#17
The drawing shows a compass and
straightedge construction of –
A. a perpendicular to a given line from a point not on the line
B. a perpendicular to a given line at a point on the line
C. the bisector of a given angle
D. an angle congruent to a given angle
#18
To which point
should a line
segment from A be
drawn so that the resulting figure is a
rectangle?
A. W
B. X
C. Y
D. Z
#19
When standing
upright, Gary knows
his eyes are 6 feet
above ground level.
To determine the
depth of a well, he
stands in the position
shown. Using the
given measures, how
deep is the well?
A. 12 ft
B. 14 ft
C. 16 ft
D. 18 ft

#20

In a chess game, a knight’s move is 2
units in one direction and 1 unit in a
perpendicular direction. If a knight starts
at the origin and makes one move, which
could NOT be its location?
A. (-1, -2)
B. (1, 2)
C. (2, -1)
D. (-2, 2)
#21

What is the vertical cross section of a
cone?
A. rectangle
B. circle
C. triangle
D. square
#22

A square in a coordinate plane undergoes a
40% dilation with respect to the origin. One
corner of this square originally had
coordinates (60, 80). What are the
coordinates of the dilated image of this
corner?
A. (20, 60)
B. (24, 32)
C. (36, 48)
D. (40, 40)
#23

Which of these plane figures is NOT a
possible cross section of a cube?
A. triangle
B. hexagon
C. pentagon
D. octagon
#24

Joan wants to bisect FGH . What should
she do first?
A. Swing an arc from point F
B. Swing an arc from point G.
C. Swing an arc from point H
D. Use her straightedge to draw a segment.
#25

Scott drew a picture on a piece of paper.
The picture measured 11 inches tall and
8.5 inches across. Then Scott photocopied
his paper, using a 70% scale factor
setting. To the nearest square inch, what
was the area of the photocopied picture?
A. 70 square inches
B. 65 square inches
C. 50 square inches
D. 46 square inches
#26

To bisect PQ , John began by swinging equal
arcs from points P and Q above the segment
and labeling point X where the arcs met. What
should John do next?
A. Use a straightedge to draw a line segment from
X to P and a line segment from X to Q.
B. Use a straightedge to draw a line segment from
X to the point in the middle of PQ
C. Swing an arc from point X.
D. Swing equal arcs from points P and Q below the
segment.
#27

A cylinder is cut by a plane to form a cross
section shaped like an ellipse. How could
the plane that formed the cross-section
have cut the cylinder?
A. parallel to a base of the cylinder
B. perpendicular to a base of the cylinder
C. slightly tilted away from a base of the
cylinder
D. none of the above
#28

A line segment has length of 36 cm. If Lu
bisects the segment, what is the length
of each segment he constructs?
A. 12 cm
B. 18 cm
C. 36 cm
D. 72 cm
#29

A rectangle has an area of 30 square feet.
A similar rectangle has an area of 270
square feet. What is the scale factor for
these similar rectangles?
A. 3
B. 9
C. 81
D. 240
#30

A rectangle is translated 3 inches directly
above the plane in which it lies. The
vertices of the two rectangles are then
connected with four line segments. What
three-dimensional figure is formed?
A. cone
B. cube
C. cylinder
D. rectangular prism
#31

What three-dimensional figure will be formed if
the rectangle shown is rotated about the line
shown?
A. cone
B. cylinder
C. cube
D. sphere
#32

Which set of transformations returns a
given figure to its original location?
A. translation 2 units left, then 3 units up,
then 3 units right, then 2 units down
B. reflection across the y-axis, then the xaxis, then the y-axis, and then the x-axis
C. 180° counterclockwise rotation
D. 90° clockwise rotation, then reflection
across the line y = x
#33

Triangle JKL is located at J(1, 1), K(1, 5)
and L(5, 5). Point K will be translated one
unit up and 6 units to the right. What
shape will triangle J’K’L’ become?
A. right triangle
B. acute triangle
C. obtuse triangle
D. equilateral triangle
#34

Which of these shapes can be created
using two congruent isoceles triangles?
A. rhombus
B. rectangle
C. trapezoid
D. parallelogram
#35

If ADH  PXV, how many pairs of
congruent corresponding parts must they
have?
A. 1
B. 3
C. 6
D. 12