Page 695 - Basic College Mathematics with Early Integers

672 C HAPTE R 9 I GEOMETRY

PRACTICE 2 Example 2 Find the ratio of corresponding sides for the similar triangles
Find the ratio of corresponding ABC and DEF.
sides for the similar triangles D
QRS and XYZ. A
Q

B C E F
S 12 ft 19 ft
R 9 m
X Solution: We are given the lengths of two corresponding sides.Their ratio is

12 feet 12
=
19 feet 19
Z
Y 13 m
Work Practice 2

Objective Finding Unknown Lengths of Sides
in Similar Triangles

Because the ratios of lengths of corresponding sides are equal, we can use propor-
tions to find unknown lengths in similar triangles.

PRACTICE 3 Example 3 Given that the triangles are similar, find the missing length n.
Given that the triangles are
similar, find the missing length n. n
a. 10 3
n 2
4
10 5 Solution: Since the triangles are similar, corresponding sides are in proportion.
Thus, the ratio of 2 to 3 is the same as the ratio of 10 to n,or
b.
5 2 10
=
9 n
3
To find the unknown length n, we set cross products equal.
n
6
s 10
n

#
#
2 n = 3 10 Set cross products equal.
#
2 n = 30 Multiply.
30
n = Divide 30 by 2, the number multiplied by n.
2
n = 15
The missing length is 15 units.
Copyright 2012 Pearson Education, Inc.
Work Practice 3

Answers
9 10 1
2. 3. a. n = 8 b. n = or 3
13 3 3