Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Solve each proportion.
1.
2.
x 45
x 20
3.
4.
x 4
x 2
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Problem of the Day A plane figure is dilated and
gets 50 larger. What scale factor should you
use to dilate the figure back to its original
size? (Hint The answer is not .)
1 2
2 3
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Learn to find measures indirectly by applying the
properties of similar figures.
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Vocabulary
indirect measurement
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Sometimes, distances cannot be measured directly.
One way to find such a distance is to use
indirect measurement, a way of using similar
figures and proportions to find a measure.
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Additional Example 1 Geography Application
Triangles ABC and EFG are similar. Find the
length of side EG.
Triangles ABC and EFG are similar.
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Additional Example 1 Continued
Triangles ABC and EFG are similar. Find the
length of side EG.

Set up a proportion.
Substitute 3 for AB, 4 for AC, and 9 for EF.

3x 36
Find the cross products.

Divide both sides by 3.
x 12
The length of side EG is 12 ft.
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Check It Out Example 1
Triangles DEF and GHI are similar. Find the
length of side HI.
2 in
Triangles DEF and GHI are similar.
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Check It Out Example 1 Continued
Triangles DEF and GHI are similar. Find the
length of side HI.

Set up a proportion.
Substitute 2 for DE, 7 for EF, and 8 for GH.

2x 56
Find the cross products.

Divide both sides by 2.
x 28
The length of side HI is 28 in.
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Additional Example 2 Problem Solving Application
A 30-ft building casts a shadow that is 75 ft
long. A nearby tree casts a shadow that is 35 ft
long. How tall is the tree?
The answer is the height of the tree.
List the important information
The length of the buildings shadow is 75 ft.
The height of the building is 30 ft.
The length of the trees shadow is 35 ft.
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Additional Example 2 Continued
Use the information to draw a diagram.
h
Draw dashed lines to form triangles. The building
with its shadow and the tree with its shadow form
similar right triangles.
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Additional Example 2 Continued
30 75
h 35
Corresponding sides of similar figures are
proportional.

75h 1050
Find the cross products.

Divide both sides by 75.
h 14
The height of the tree is 14 feet.
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Additional Example 2 Continued
Look Back
75 30
Since 2.5, the buildings shadow is 2.5
times its height. So, the trees shadow should
also be 2.5 times its height and 2.5 of 14 is 35
feet.
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Check It Out Example 2
A 24-ft building casts a shadow that is 8 ft
long. A nearby tree casts a shadow that is 3 ft
long. How tall is the tree?
The answer is the height of the tree.
List the important information
The length of the buildings shadow is 8 ft.
The height of the building is 24 ft.
The length of the trees shadow is 3 ft.
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Check It Out Example 2 Continued
Use the information to draw a diagram.
h
Draw dashed lines to form triangles. The building
with its shadow and the tree with its shadow form
similar right triangles.
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Check It Out Example 2 Continued
24 8
h 3
Corresponding sides of similar figures are
proportional.

72 8h
Find the cross products.

Divide both sides by 8.
9 h
The height of the tree is 9 feet.
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Check It Out Example 2 Continued
Look Back
8 24
1 3
Since , the buildings shadow is
times its height. So, the trees shadow should
also be times its height and of 9 is 3
feet.
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1 3
1 3