Name
LESSON
Date
Class
Practice B
5-5 Similar Figures
1. Are any of these triangles similar?
Q
60°
6 ft
V
X
12 ft
8.5 ft
30°
R
45°
10.4 ft
S
T
6 ft
45°
6 ft
3 ft
60°
Z
5.2 ft
6 ft
30°
W
Y
2. A photo is 12 in. wide by 18 in. tall. If the width is
scaled down to 9 inches, how tall should the
similar photo be?
3. An isosceles triangle has a base of 20 cm
and legs measuring 36 cm. How long are the legs
of a similar triangle with base measuring 50 cm?
4. A picture of a school’s mascot is 18 in. wide and 24 in.
long. It is enlarged proportionally to banner size. If
the width is enlarged to 63 in., what is the length of
the banner?
5. Carol has a 24 cm 36 cm photo that she reduces
3
to 4 of its size. What are the dimensions of the
new photo?
6. Erik is drawing a picture of his school’s basketball
court. The actual basketball court is 84 ft long and
50 ft wide. If Erik draws the court with a length of
21 in., what will be the width?
7. IMAX theaters have the world’s largest screens.
There are numerous IMAX theaters around the world.
The Henry Ford Museum in Dearborn, Michigan
hosts an IMAX theater with a 60 ft 84 ft screen.
If a classroom projection screen were changed to
be in direct proportion with the IMAX screen at the
Henry Ford Museum, the dimensions
would be 5 ft ___ ft.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
42
Holt Mathematics
Practice B
5-5 Similar Figures
Practice A
5-5 Similar Figures
LESSON
LESSON
1. Which triangles are similar to ABC?
1. Are any of these triangles similar?
A
28° 10
110°
6
14
C
X
110°
R
42° 28° 5
3 42° 38°
B
7 S
T
8
110°
10
J
6
42° 28°
Y
16
Z
Q
100°
12
14
M
42°
K
30°
6
S
B
3
U
T
D
C
9
B
3
N
1
Q
C
O 3
P
E
D
NOPQ and BCDE
2
1
3. A room is 36 ft long and 18 ft wide. What is the
length to width ratio?
4. An isosceles triangle has a base of 8 inches and
legs measuring 12 inches. How wide is the base
of a similar triangle with legs measuring 36 inches?
24 in.
5. A photo that is 8 in. wide and 12 in. long is
enlarged to a poster. If the width is enlarged
to 24 in., what is the length of the poster?
36 in.
6. Clyde makes a copy of an 8 in. 10 in. photo,
3
reducing it to 4 of its size. What are the
dimensions of the new photo?
2 ft
41
2. A photo is 12 in. wide by 18 in. tall. If the width is
scaled down to 9 inches, how tall should the
similar photo be?
13.5 in.
3. An isosceles triangle has a base of 20 cm
and legs measuring 36 cm. How long are the legs
of a similar triangle with base measuring 50 cm?
90 cm
4. A picture of a school’s mascot is 18 in. wide and 24 in.
long. It is enlarged proportionally to banner size. If
the width is enlarged to 63 in., what is the length of
the banner?
84 in.
Holt Mathematics
Similar Polygons
R
42
B
X
x
21
Holt Mathematics
same shape
corresponding angles are congruent
A A', B B', C C'
30° C'
32
56
30° C
A
S
36
C 24
usually different size
corresponding sides are in proportion
60°
60°
B
A
14
A'
B
AB
BC
AC
A'B'
B'C'
A'C'
B'
T
C
Y D
7
Review for Mastery
5-5 Similar Figures
2.
Z
12.5 in.
LESSON
1.
W
18 cm 27 cm
42
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
The figures in each pair are similar. Solve for x.
27
Y
7. IMAX theaters have the world’s largest screens.
There are numerous IMAX theaters around the world.
The Henry Ford Museum in Dearborn, Michigan
hosts an IMAX theater with a 60 ft 84 ft screen.
If a classroom projection screen were changed to
be in direct proportion with the IMAX screen at the
Henry Ford Museum, the dimensions
would be 5 ft ___ ft.
Practice C
5-5 Similar Figures
A
30°
W
6. Erik is drawing a picture of his school’s basketball
court. The actual basketball court is 84 ft long and
50 ft wide. If Erik draws the court with a length of
21 in., what will be the width?
LESSON
x
45°
6 ft
T
Z
5.2 ft
6 ft
5. Carol has a 24 cm 36 cm photo that she reduces
3
to 4 of its size. What are the dimensions of the
new photo?
6 in. 7.5 in.
7. The White House, built 1792, is the oldest federal
building in Washington, D.C. The building has
undergone extensive remodeling over the years.
The main building is four stories high and is about
170 ft long by 85 ft wide. If a replica of the White
House were made with a length of 4 ft, what would
be the width of the replica?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
S
6 ft
QRS XZY
2. Which rectangles are similar to RSTU?
R
2
45°
8.5 ft
10.4 ft
R
8
3 ft
60°
X
12 ft
6 ft
ABC RST JMK
A
V
60°
Complete to tell if the polygons are similar.
x 18
1. a. corresponding angles: A and
x 63
3.
A
25
B
P
x
18
D
C
T
, D and
, B and
72
B M
35
6
BC
AB
7.5 , EF
FG
P
D
x
C
63
O
B
,
H
x 30
6
7.5
6. A house measures 90 ft long by 66 ft wide. If the
blueprints indicated 1 cm 3 ft, what are the
dimensions of the house on the blueprints?
what would the dimensions of the replica be?
8. The Golden Gate Bridge in California is 8,976 ft
long and 90 ft wide. What would be the length of a
reproduction of the bridge if the width were 2 ft?
Round the answer to the nearest tenth of a unit.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
43
Copyright © by Holt, Rinehart and Winston.
66°
114°
D
8 cm
G
114°
66°
8
7.5 cm
10
66°
114°
E
10 cm
H
60 60
e. Are the parallelograms similar? Explain.
yes; corresponding s congruent, corresponding sides proportional
AB 18 cm,
BC 10 cm,
AC 14 cm
Use a proportion to find a missing dimension. Corresponding sides are in proportion.
AB
BC
DE
EF
6
BC
9
15
30 cm long by 22 cm wide
C
F
40°
? 70°
A 6 mB
BC 10 m
40°
15 m
70°
70°
D 9mE
70°
9(BC) 90
7. M. C. Escher, a Dutch painter, explored mathematical
symmetry through many of his works. In 1931, he
painted Carruba Tree. The picture is 32 cm by 24.2 cm.
1
If a replica were made reducing it to 4 of its size,
8
10
yes; equal cross products x 40
114°
F
8
6
CD
AD
10 , 7.5 , GH
EH
d. Are the corresponding sides proportional? Explain.
5. In XYZ, XY = 27 cm, YZ = 15 cm, and
XZ = 21 cm. If ABC XYZ and the ratio of the
corresponding sides of the triangles is 2 to 3,
find the lengths of AB
, B
C
, and AC
.
C
66°
A
yes
c. The ratio of each pair of corresponding sides is:
N
21.6
S
F
6 cm
b. all corresponding angles congruent?
A
R
G
C and
4.
E
Complete to find the missing dimension.
8 cm 6.05 cm
MA
RO
14
MH
8
6
MH
RE
2.
199.5 ft
8
Holt Mathematics
(MH) MH Copyright © by Holt, Rinehart and Winston.
All rights reserved.
87
E
P
6 in.
?
M
84
10.5
T
H
R
14 in.
8 in.
O
A
in.
44
Holt Mathematics
Holt Mathematics