Geometry 2nd Nine Weeks Practice Exam
1) Triangles ACE and BCD are similar. What is x equal to?
A
10
B
6
14
x
E
C
D
2) The flagpole is about 15 feet tall. At 4pm it cast a shadow that is 20 feet long and the tree’s shadow is 45 feet
long. About how tall is the tree?
x
15
45
20
3) The location of point B after translation is (3, -1).
What is the rule that describes this translation?
4) What is the sine of angle x in this rectangle?
b
O
c
B
a
x˚
Y
5) What is the perimeter of this right triangle?
55
33
1
6) Triangle A’B’C’ is a translation of triangle ABC.
7) Segments BE and BC are radii of circle B
What transformation created triangle A’B’C’?
Chord AC is 12in long. What is the length of DE?
(Round to the tenths place)
A’
C’
A
B’
C
B
8in
B
A
D
C
E
8) Triangle GHK is a right tringle.
9)Karen drew this triangle: Write and expression
What is cos H, to the nearest hundredth?
that proves that the triangle is impossible.
G
8
13
4
5
H
12
15
K
10) Heather drew this figure and the accompanying equtions. Which equation must also be true?
E + Y + K = 180
Hint (Use the transitive property of equaltity)
K + P = 180
E+Y
K
P
2
11) Triangles XYZ and ATE are similar. What is the measure of angle Y, rounded to the nearest tenth?
T
Y
X
Z
20
A
12) This triangle is translated (x + 2, y – 1), then
is reflected across the y- axis, and finally is reflected
across the x-axis. What is are the final
coordinates of point J?
14) Fill in the proof below:
8
E
13) Reflecting over what line would carry the
triangle onto itself?
15) Answer the following questions:
1) What are the similarities and differences between
congruent and similar figures?
2) What type of figure does each transformation create?
Given
Given
Alternate
Interior Angles
Reflexive
property
ASA
Transformation
Translation
Rotation
Reflection
Dilation
Vertical Stretch
Horizontal Stretch
Similar, Congruent, Neither
CPCTC
3
16) Apply a dilation with a scale factor of ½ to triangle XYZ. Let the image be X”Y”Z”. Which one of the following
equations is true?
a) mY’ = ½ (mY)
b) YZ = ½ (Y’Z’)
C) mY = ½ (mY’)
D) Y’Z’ = ½ (YZ)
17) A wheelchair ramp has an angle of elevation of 15˚. If the ramp is 20ft long, what is the change in elevation, x?
20ft
x
15˚
18) What is tan W, to the nearest hundredth?
W
20
19) What is the sine angle z in the relationship?
P
z˚
c
25
a
15
Q
d
20) Given a line drawn on a graph, describe what changes would occur with the following rotations:
a) 90˚
b) 180˚
c) 270˚
d) 360˚
4
21) What series of transformation will map triangle XYZ onto GHI?
`
G
A) Reflect over the y-axis and dilate by a scale factor of 1/2
H
B) Rotate 180˚ and dilate by a scale factor of ½
I
c) Rotate 90˚ clockwise and dilate by a scale factor of ½
d) Reflect over the x-axis and dilate by a scale factor of 1/2
Z
X
Y
22) The table shows the statements and reasons out of order. What is the correct order?
Given  1 and  2 are a liner pair
 1 and  3 are a liner pair
1
3
Prove  2 ≅ 3
Statements
2
4
Reasons
Given
23) Construct an angle bisector with only a compass and a straightedge.
24) Given Circle R with radius = r, and Circle M with radius = m, and both circles have the same center, write a
dilation to prove the two circles are similar.
Dilate circle ____ by a scale factor of ______
5