7th Grade Math

Lesson 3A Similarity and Proportional Reasoning 295

Find Missing Measures

If RST ∼ XYZ, find the length of

−−

XY.

Since the two triangles are similar,

5

34

9 :

;

5 m 15 m

n m

6 m 18 m

4 m

the ratios of their corresponding

sides are equal. Write and solve

a proportion to find XY.

_XZRT = _XYRS Write a proportion.

_ 186 = _^4 n Let n represent the length of −−XY. Then substitute.

6 n = 18(4) Find the cross products.

6 n = 72 Simplify.

n = 12 Divide each side by 6. The length of

−−

XY is 12 meters.

b. If ABC ∼ EFD, find the

4 ft

5 ft

3 ft

%

35 ft & '

28 ft

"

# $

n ft

length of

−−

AC.

Indirect measurement uses similar figures to find the length, width,

or height of objects that are too difficult to measure directly.

GEYSERS Old Faithful in

Yellowstone National Park

shoots water 60 feet into the

air and casts a shadow of

42 feet. What is the height

of a nearby tree that casts a

shadow 63 feet long? Assume

the triangles are similar.

_ 60 x = _ 4263 Write a proportion.

42 x = 60(63) Find the cross products.

42 x = 3,780 Simplify.

x = 90 Divide each side by 42.

The height of the tree is 90 feet.

c. PHOTOGRAPHY Destiny wants to

4 in.

5 in.

2 in.

resize a 4-inch-wide by 5-inch- x in.

long photograph so that it will fit

in a space that is 2 inches wide.

What is the new length?

Similarity Corresponding

angles are written in the

same order.

RST ∼ XYZ

63 ft 42 ft

60 ft

x ft

293_303_C05_L3_895130.indd 295 12/29/09 1:09 PM