Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Find the missing value in each
proportion. 1. 2. 3. 4.

t 15
k 5
n 56
x 84
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Problem of the Day Bryce, Kate, and Annie have
drawn rectangles. Each side of Bryces rectangle
is twice the size of one side of Kates. The same
side of Kates rectangle is congruent to one side
of Annies. One side of Annies rectangle is
congruent to one side of Bryces. Which two
rectangles could be congruent?
Kates and Annies
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Learn to use proportions and similar figures to
find unknown measures.
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Insert Lesson Title Here
Vocabulary
indirect measurement
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One way to find a height that you cannot measure
directly is to use similar figures and
proportions. This method is called indirect
measurement.
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Additional Example 1 Using Indirect
Measurement Use the similar triangles to find the
height of the tree.
Write a proportion using corresponding sides.

h 2 6 7
The cross products are equal.
2h 42
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.

h 21
The tree is 21 feet tall.
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Try This Example 1 Use the similar triangles to
find the height of the tree.
Write a proportion using corresponding sides.

h 3 6 9
The cross products are equal.
3h 54
h is multiplied by 3.
6 ft. h
Divide both sides by 3 to undo multiplication.

3 ft. 9 ft.
h 18
The tree is 18 feet tall.
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Additional Example 2 Measurement Application A
rocket casts a shadow that is 91.5 feet long. A
4-foot model rocket casts a shadow that is 3 feet
long. How tall is the rocket?
Write a proportion using corresponding sides.

4 91.5 h 3
The cross products are equal.
366 3h
h is multiplied by 3.
Divide both sides by 3 to undo multiplication.

122 h
The rocket is 122 feet tall.
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Try This Example 2 A building casts a shadow
that is 72.5 feet long when a 4-foot model
building casts a shadow that is 2 feet long. How
tall is the building?
Write a proportion using corresponding sides.

4 72.5 h 2
The cross products are equal.
290 2h
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
h

4 ft
145 h
72.5 ft 2 ft
The building is 145 feet tall.
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Insert Lesson Title Here
Lesson Quiz
1. On a sunny day, a telephone pole casts a
shadow 21 ft long. A 5-foot-tall mailbox next to
the pole casts a shadow 3 ft long. How tall is
the pole? 2. On a sunny afternoon, a goalpost
casts a 75 ft shadow. A 6.5 ft football player
next to the goal post has a shadow 19.5 ft long.
How tall is the goalpost?
35 feet
25 feet