Lesson 11.1 • Similar Polygons
Name
Period
Date
All measurements are in centimeters.
1. HAPIE NWYRS
AP _____
H
EI _____
2. QUAD SIML
6 A
5
I
E
Y
S
A
D
M
25
13
mU _____
75°
mA _____
R
21
L
I 85°
mD _____
24
N
YR _____
S
8
MI _____
W
18
SN _____
120°
SL _____
P
4
Q
20
3. Copy PQRS onto your paper. Use a compass and straightedge
R
S
to construct a similar quadrilateral with twice the perimeter
of PQRS. Explain your method.
P
4. PQS QRS. What’s wrong with this
Explain why or why not.
Q
P
120°
120°
3
8
60°
60°
9
5
3
Q
5. Are the pair of polygons similar?
picture? Explain.
6
U
120°
60°
15
R
S
In Exercises 6–8, decide whether or not the figures are similar. If they
are not, explain why.
6. ABC and ADE
7. JKON and JKLM
A
2
B
D
J
6
3
2
4
E
8
3
N
C
5 K
E
A
3
B
8
4
O
10
G
14
12
M
8. ABCD and AEFG
4
7
F
4
3
20
L
D
7
C
9. Copy DART and center O onto your paper. Use geometry tools
T
to draw a dilation image with scale factor 1.5. Measure DA, RT,
DA
RT
DA, and RT. Calculate DA and RT . Are the results what you
expected? Explain.
R
A
D
O
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Lesson 11.2 • Similar Triangles
Name
Period
Date
All measurements are in centimeters.
M
1. TAR MAC
C
3
MC _____
A
2
R
2. XYZ QRS
T
7
3. ABC EDC
4. TRS TQP
Q _____
A _____
TS _____
QR _____
CD _____
QP _____
QS _____
AB _____
Y
19.5
X
6
Z
28.6
A
R 7.8
E
3
21 _4
B
12.1
T
8
R
17
16
C
30
P
Q
1
22 _2
2
9 _3
S
S
Q
D
For Exercises 5 and 6, refer to the figure at right.
16
5. Explain why CAT and DAG are similar.
D
A
12 G
6. CA _____
C
7. x _____
48
T
8. Are the two triangles similar?
Explain why or why not.
1
18 _2
11
3
5
4 _8
x
3.75
4
In Exercises 9–12, write an equation for two triangles that are similar.
Explain why each pair is similar.
9.
10.
B
11.
Q
N
P
R
C
A
D
12.
M
E
T
L
O
R
I
K
G
H
S
13. Draw a trapezoid with both diagonals. Name a pair of similar triangles.
70
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Lesson 11.3 • Indirect Measurement with Similar Triangles
Name
Period
Date
1. At a certain time of day, a 6 ft man casts a 4 ft shadow. At the same
time of day, how tall is a tree that casts an 18 ft shadow?
2. If a 5 ft 10 in. person casts a 7 ft 4 in. shadow, how tall is a person
who, at the same time, casts a 6 ft 8 in. shadow? Give your answer to
the nearest inch.
3. Driving through the mountains, Dale has to go up and over a high
mountain pass. The road has a constant incline for 734 miles to the
top of the pass. Dale notices from a road sign that in the first mile
he climbs 840 feet. What is the height of the mountain pass?
(5280 ft 1 mi)
4. Sunrise Road is 42 miles long between the edge of Moon Lake
and Lake Road and 15 miles long between Lake Road and
Sunset Road. Lake Road is 29 miles long. Find the length of
Moon Lake.
Sunrise Road
Moon
Lake
Lake
Road
Sunset Road
5. Marta is standing 4 ft behind a fence 6 ft 6 in. tall. When
she looks over the fence, she can just see the top edge of a
building. She knows that the building is 32 ft 6 in. behind
the fence. Her eyes are 5 ft from the ground. How tall is
the building? Give your answer to the nearest half foot.
Fence
Building
5 ft
6 ft 6 in.
4 ft
32 ft 6 in.
6. You need to add 5 supports under the ramp, in addition to
the 3.6 m one, so that they are all equally spaced. How long
should each support be? (One is drawn in for you.)
Ramp
Support
3.6 m
9.0 m
7. Stretch your arm out straight in front of you and hold your
thumb straight up. Close one eye and look at a distant object.
Without moving your arm (or thumb), switch eyes. What
appears to happen? Measure the distance between your eyes
and the distance between one eye and your thumb. Explain
how, with one other piece of information, you can now use
similar triangles to estimate the distance to the distant object.
What else do you need to know?
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CHAPTER 11
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Lesson 11.4 • Corresponding Parts of Similar Triangles
Name
Period
Date
All measurements are in centimeters.
1. ABC PRQ. M and N
2. The triangles are similar.
are midpoints. Find h and j.
Find the length of the three sides of the
smaller triangle to two decimal places.
R
1.5
1.2
h
P
Q
N
B
12
3.2
2.4
j
A
8
C
M
3
10
of ABC has measure 12.4 cm. Median AD
of the
3. Median AD
dilation image ABC has measure 3.1 cm. If AB 16.8 cm,
AB _____.
4. ABC WXY
5. BK 6 cm, BL 4 cm, and MN 1 cm.
WX _____
AD _____
DB _____
YZ _____
Find AC.
B
XZ _____
K
C
L
O
14
Y
28
16
A
A
D
B
24
W
12
C
M N
Z
X
6. Draw a segment on your paper. Use construction tools to divide your
segment into two parts with ratio 3:5. Explain your method.
7. Find x and y.
10
x
5
8. Find a, b, and c.
9. Find CB, CD, and AD.
A
y
3
c
25
7
6
8
C
b
D
B
4
a
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Lesson 11.5 • Proportions with Area and Volume
Name
Period
Date
All measurements are in centimeters unless otherwise indicated.
In Exercises 1–4, decide whether or not the two solids are similar.
1.
2.
2
1 _3
4
20
3
16
5
8
12
1
2 _3
6
3
32
5
3.
4.
1
x
y
2.5
8
y
x
6
1.5
Area of square SQUA
Area of square LRGE
Area of circle P
Area of circle O
5. _____ 6. _____
G
E
7. RECT ANGL
12␲
A
S
Area of RECT
_____
Area of ANGL
C
T
L
10
P
2␲
3
Q
L
U
5
G
4
A
N
R
R
E
O
8. The ratio of the corresponding midsegments of two similar trapezoids
is 4:5. What is the ratio of their areas?
9. The ratio of the areas of two similar pentagons is 4:9. What is the ratio
of their corresponding sides?
10. The corresponding heights of two similar cylinders is 2:5. What is the
ratio of their volumes?
11. The ratio of the weights of two spherical balls is 27:64. What is the
ratio of their radii?
12. If ABCDE FGHIJ, AC 6 cm, FH 10 cm, and area of
ABCDE 320 cm2, then area of FGHIJ _____.
13. A rectangular prism aquarium holds 64 gallons of water. A similarly
shaped aquarium hold 8 gallons of water. If a 1.5 ft2 cover fits on the
smaller tank, what is the area of a cover that will fit on the larger tank?
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CHAPTER 11
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Lesson 11.6 • Proportional Segments Between Parallel Lines
Name
Period
Date
All measurements are in centimeters.
BC
?
2. Is XY
1. x _____
A
MK
?
3. Is XY
M
A
3
2
8
6
9
X
4.5
3
4. NE _____
N
12.5
60
6. a _____
PQ _____
b _____
RI _____
M
8
12
A
15
5
Q
b
5
4.5
3
E
I
R
8. x _____
9. p _____
EB _____
y _____
q _____
R
E
B
S
y
15
10
30
2
12
9
5
T
q
3
4
x
12
4
p
10. x _____
11. AC _____
12. x _____
y _____
XY _____
y _____
50°
Explain why mYXB 90°.
3.5
2
4.5
5
3
3
3
3
x
26
x
Y
y
A
CHAPTER 11
3
3
C
50°
74
T
a
A
7. RS _____
15
O
n
10
P
30
48
Y
5. PR _____
T
3
P
M
K
C
B
T
P
40
Y
X
ᐉ
x
24
X
8
y
13
12
B
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