NAME: _________________________
Geometry Chapter 11 Review
DATE: _____________________
Place all answers in your HW notebook. All final
answers are on Kruzich’s website. You should be
checking your work! SHOW ALL WORK!!
4. Draw the image of ABC after a dilation of scale
factor 4.
8 19
1. Solve the proportion.

12 p
2. A city is developing plans for a new community
sports facility. Community members can submit
suggestions for the new facility, along with basic
scale drawings of their ideas. Julio wants to include
a new 15- by 30-meter basketball court in the
athletic center. He is submitting a scale drawing on
an 8.5- by 11-inch sheet of paper. Which scale
should Julio use to create as large a drawing as
possible on the paper?
[A]
1
in.  1 m
4
[B]
3
in.  1 m
8
10
9
8
7
6
5
4
3 B
2
1
C
A
1 2 3 4 5 6 7 8 9 10
5. Are ABC and FDE similar? Explain why or
why not.
B
25 mm
F
D
48 mm
14 mm
1
[C] in.  1 m
2
7 mm
24 mm
E
A
5
in.  1 m
16
[D]
PERIOD: _______________
3. QPR ~ OMN
Find a, b, and c if the perimeter of MON is 45
inches. All measurements are in inches.
O
Q
50 mm
C
6.In RST , RS  10 centimeters, mR  48, and
mS  30.
In UVW , UW  30 centimeters, mW  48, and
mU  30. Which statement of similarity
identifies the two similar triangles and gives the
correct justification of their similarity?
c
28 in.
b
[A] RST  UVW; AA similarity
14 in.
M
P
21 in.
a
N
[B] RST ~ VWU ; SAS similarity
R
[C] RST ~ WUV ; AA similarity
[D] The triangles are not similar.
1
Kruzich ‘12
Geometry Chapter 11 Review
7. Marcia wants to measure the height of the
flagpole at her school. She places a mirror on the
ground 50 feet from the flagpole, then walks
backward until she is able to see the top of the
flagpole in the mirror. Her eyes are 5 feet above the
ground, and she is 9 feet from the mirror. Find the
height of the flagpole to the nearest tenth.
11. VOL ~ UME
The area of UME is 3888 square meters. Find the
area of VOL.
M
O
52 m
78 m
V
8. BAE ~ HIE
Find x.
E
U
B
L
A
12. If the sides of a square are made one-seventh the
original length, what fraction of the original area is
the new area?
x
36 m
E
1
the original area
70
1
[B]
the original area
28
1
[C] the original area
7
1
[D]
the original area
49
[A]
24 m
12 m
I
H
9. Find the value of y that will allow ICE to be
similar to AGE.
I
C
13. The ratio of the volumes of two similar
343
triangular prisms is
. What is the ratio of their
64
heights?
y
4.5cm
E
7.2cm
4.8cm
G
A
10. Find y. Round your answer to the nearest two
decimals.
8m
B
C
y D
14. These right cylinders are similar.
The volume of the large cylinder
is 1536 cubic meters.
a. Find the volume of the small cylinder.
b. Find the ratio of the volume of the larger cylinder
to the volume of the smaller cylinder.
c. Find H.
4m
13 m
11 m
12m
2
Kruzich ‘12
A
Geometry Chapter 11 Review
15. Using a straightedge and compass,
divide FG into 3 equal parts.
G
19. Find the slope of a line parallel to the line
through the points – 3, – 10 and – 9, 2 .
b
g b
g
20. What is the slope of the line perpendicular to the
line 4 x  2 y  7?
21. Solve the equation and check your solution.
1  2 4x  8  9x  7
b
g
22. Write the equation of the line below in both
point-slope form and slope-intercept form.
F
y
10
16. Determine which coordinates are the midpoints
of the sides of the quadrilateral.
y
5
–10

–5
5
–5




10 x
–10




 x
23. Solve the system of equations.

1
y  x4
3
y  2x 1

17. Find the slope of the line passing through the
points A – 7, – 6 and B 6, 3 ?
24. Solve the system of equations.
18. Use slope triangles to calculate the slope of the
graphed line.
25. Solve the system of equations.
b
b g
g
y
10
–5
2x  5 y  5
3x  5 y  5
26. Solve the system of equations.
5
–10
y  5x  2
2x  3y  7
5
10 x
x  4 y  21
3x  y  19
–5
–10
3
Kruzich ‘12
Geometry Chapter 11 Review
27. Find the equation of the line containing the
median from B to AC. Write the equation of the
line below in both point-slope form and slopeintercept form.
b
g
b
g
b
g
33. The rectangular shipping crates below are
similar.
a. Find the similarity ratio of the crate on the left to
the crate on the right.
b. Find the ratio of their volumes.
A  – 11, – 17 , B  – 14, 8 , C  – 13, – 15
28. Sketch and label a diagram to factor the
expression.
2
x  7 x  12
7 ft
9 ft
7 ft
29. Solve the equation.
2
y  2 y  13y  56
2 ft
34. Are rectangles KLMJ and BCDA similar?
Explain why or why not.
K
30. Rationalize the following and be sure to write
with no perfect squares under the radical.
[A]
[C]
11
2
5
3
[B]
[D]
12
2
6
3
31. Solve for b when a 2  b2  c2
Given c  34 m, find the values of b
for a  36
. m, a  8 m, and a  4.5 m.
Round to the nearest hundredth if necessary.
32. Write the converse, inverse and the
contrapositive of the following two statements. Also
determine if the new statements are true or false.
a. If two angles of one triangle are congruent to
two angles of another triangle, then the triangles
are similar.
b. If it is raining outside, then it is cloudy.
L
C
B
18 cm
J
6 cm
A
10 cm
D
M
33 cm
35. Are rectangles KLMJ and BCDA similar?
Explain why or why not.
K
L
B
6 cm
A
30 cm
J
C
9 cm
D
M
45 cm
36. Find the values of x and y. Write your answer as
a reduced radical…no decimals!!
N
x
22 mm
45°
30°
M
37. Solve the proportion.
y
P
x x2

20
28
4
Kruzich ‘12
Geometry Chapter 11 Review
[1] 28.5
[15]
G
[2] [D]
[3] a  15 in. , b  10 in., c  20 in.
[4]
10
9 B
8
7
6
5
4
3
2
1
A
F
b
gb gb
gb
C
[17]
9
13
1 2 3 4 5 6 7 8 9 10
[5] Yes; three sides of the first triangle are
proportional to three sides of the second triangle.
[6] [C]
[18] 
5
11
[19] 2
1
2
[7] 27.8 ft
[20] 
[8] 18 m
[21] x  10
[9] 3.0 cm
[10] 4.33 m
[22] y  2  2( x  1) and others…
And slope-intercept is y  2 x  4
[11] 1728 m2
[23] (3, 5)
[12] [D]
[24] (-1, -3)
[13]
g
[16] – 3, 1 , 1, 3 , 4, – 1 , 0, – 3
7
4
[14] a. 192 m3
8
b.
1
c. 24 m
1
5
[25] (2,  )
[26] (-5, 4)
[27] y  16  12( x  12) or y  8  12( x  14)
then slope-intercept is y  12 x 160
5
Kruzich ‘12
Geometry Chapter 11 Review
b gb g
[28] x  4 x  3
[29] y  8 or y  7
11 2
[30] [A]
2
[B] 6 2
5 3
[C]
3
[D] 2 3
[34] No, they are not similar. Although the
corresponding angles are all congruent, the
corresponding sides are not proportional.
[35] Yes, they are similar. The corresponding
angles in both polygons are congruent and the
corresponding sides are proportional.
[36]
x  11 2
y  11  11 3
[37] 5
[31] b  c2  a 2
33.81, 33.05, 33.7
[32] a. CONVERSE: If the triangles are similar,
then two angles of one triangle are congruent to two
angles of another triangle. TRUE
INVERSE: If two angles of one triangle are NOT
congruent to two angles of another triangle, then the
triangles are NOT similar. TRUE
CONTRAPOSITIVE: If the triangles are NOT
similar, then two angles of one triangle are NOT
congruent to two angles of another triangle. TRUE
b. CONVERSE: If it is cloudy outside, then it is
raining. FALSE
INVERSE: If it is NOT raining outside, then it is
NOT cloudy. FALSE
CONTRAPOSITIVE: If it is NOT cloudy outside,
then it is NOT raining. TRUE
[33] a.
b.
7
2
343
8
6
Kruzich ‘12