Learn to use similar figures to find unknown lengths'

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Learn to use similar figures to find unknown
lengths.
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Insert Lesson Title Here
Vocabulary
indirect measurement
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Indirect measurement is a method of using
proportions to find an unknown length or distance
in similar figures.
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Additional Example 1 Finding Unknown Lengths in
Similar Figures
Find the unknown length in similar figures.
AC QS
AB QR

Write a proportion using corresponding sides.
12 48
14 w

Substitute lengths of the sides.
12 w 48 14
Find the cross product.
Multiply.
12w 672
12w 12
672 12

Divide each side by 12 to isolate the variable.
w 56
QR is 56 centimeters.
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Insert Lesson Title Here
Try This Example 1
Find the unknown length in similar figures.
x
Q
R
10 cm
A
B
24 cm
12 cm
D
C
T
S
AC QS
AB QR

Write a proportion using corresponding sides.
12 24
10 x
Substitute lengths of the sides.

12 x 24 10
Find the cross product.
12x 240
Multiply.
12x 12
240 12
Divide each side by 12 to isolate the variable.

x 20
QR is 20 centimeters.
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Additional Example 2 Measurement Application
A volleyball court is a rectangle that is similar
in shape to an Olympic-sized swimming pool. Find
the length of the pool.
Let l the length of the pool.
9 25
18 l
Write a proportion using corresponding side
widths.

9 l 18 25
Find the cross products.
Multiply.
9l 450
9l 9

450 9
Divide each side by 9 to isolate the variable.
l 50
The pool is 50 meters long.
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Insert Lesson Title Here
Try This Example 2
The rectangle on the left is similar in shape to
the rectangle on the right. Find the width of the
right rectangle.
12 cm
6 cm
3 cm
?
Let w the width of the right rectangle.
6 12
3 w
Write a proportion using corresponding side
lengths.

6 w 12 3
Find the cross products.
Multiply.
6w 36
36 6
6w 6

Divide each side by 6 to isolate the variable.
w 6
The right rectangle is 6 cm wide.
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Additional Example 3 Using Indirect Measurement
City officials want to know the height of a
traffic signal. The traffic light casts a shadow
that is 45 ft long. A stop sign casts a shadow
that is 30 ft long. If the stop sign is 15 ft
high, what is the height of the traffic light?
Let x the height of the traffic light.
30 45
15 x

Write a proportion.
Find the cross product.
30 x 45 15
Multiply.
30 x 675
30x 30
675 30
Divide each side by 30 to isolate the variable.

x 22.5
The traffic light is 22.5 feet tall.
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Insert Lesson Title Here
Try This Example 3
The inside triangle is similar in shape to the
outside triangle. Find the length of the base of
the inside triangle.
Let x the base of the inside triangle.
8 2
12 x
Write a proportion using corresponding
side lengths.

8 x 2 12
Find the cross products.
8x 24
Multiply.
8x 8
24 8

Divide each side by 8 to isolate the variable.
x 3
The base of the inside triangle is 3 inches.
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Insert Lesson Title Here
Lesson Quiz
Find the unknown length in each pair of similar
figures.
J
3. These two rectangular cakes are similar in
shape. How long is the larger cake?
A
144 cm
96 cm
1.
x
C
80 cm
K
56 cm
B
84 cm
L
10 in.
x 120 cm
x
6 in.
2.
9 in.
160 cm
t
120 cm
72 cm
90 cm
x 15 inches
t 150 cm