Transcript Similar Figures and Proportions

COURSE 3 LESSON 5-5
Similar Figures and Proportions
Given that rectangle EFGH ~ rectangle WXYZ, find t.
EF EH
=
WX WZ
9
3
=
12
t
9 • t = 12 • 3
9t
36
=
9
9
t=4
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EF corresponds to WX.
EH corresponds to WZ.
Substitute.
Write the cross products.
Multiply. Then divide each
side by 9.
Simplify.
COURSE 3 LESSON 5-5
Similar Figures and Proportions
A model train set has a passenger car that is 21.6 in. long. Its
actual length is 72 ft. How long will the model for an 80-ft freight car be?
The model car and the actual car are similar. Write a proportion.
Words
model passenger car length
model freight car length
=
actual passenger car length
actual freight car length
Let x = model freight car length.
Proportion
21.6 in.
x
=
72 ft
80 ft
21.6 • 80 = 72 • x
1,728 = 72x
1,728
72x
=
72
72
24 = x
Write the cross products.
Simplify.
Divide each side by 72.
Simplify.
The length of the model freight car is 24 in.
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COURSE 3 LESSON 5-5
Similar Figures and Proportions
RST ~
PSU. Find the value of d.
Step 1 Separate the triangles as
shown at the right.
Step 2 Write a proportion using corresponding
sides of the triangles.
SR RT
=
SP PU
12
14
=
21
d
12 • d = 21 •14
12d = 294
12d
294
=
12
12
d = 24.5
Substitute.
Write the cross products.
Simplify.
Divide each side by 12.
Simplify.
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COURSE 3 LESSON 5-5
Similar Figures and Proportions
1. Are the triangles similar? Explain.
No; their sides are not proportional.
2. A model of a building is 18 in. tall and 24 in. wide. The building is 30 ft
tall. How wide is the building?
40 ft
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