Page 694 - Basic College Mathematics with Early Integers

S E C T I O N 9.6 I CONGRUENT AND SIMILAR TRIANGLES 671

Example 1 Determine whether triangle ABC is congruent to triangle DEF. PRACTICE 1
a. Determine whether triangle
D MNO is congruent to
triangle RQS.
B 8 mi
M N
13 in. 90
12 in.
12 in. 8 in. 6 mi

F
A C
13 in. 8 in.
E O
Q
Solution: Since the lengths of all three sides of triangle ABC equal the lengths
of all three sides of triangle DEF, the triangles are congruent.
8 mi
Work Practice 1
90
In Example 1, notice that as soon as we know that the two triangles are congru-
S R
ent, we know that all three corresponding angles are congruent. 6 mi
b. Determine whether triangle
Objective Finding the Ratios of Corresponding Sides GHI is congruent to triangle
in Similar Triangles JKL.
G
Two triangles are similar when they have the same shape but not necessarily the
same size. In similar triangles, the measures of corresponding angles are equal and
corresponding sides are in proportion.The following triangles are similar:

D 107 37
H I
45 m
A
45 m
14 L K
10 37 105
5 7

B C E F
6 12
J
Since these triangles are similar, the measures of corresponding angles are
equal.
Angles with equal measure: ∠A and ∠D, ∠B and ∠E, ∠C and ∠F .Also, the
lengths of corresponding sides are in proportion.
AB BC CA
Sides in proportion: = = or, in this particular case,
DE EF FD
AB 5 1 BC 6 1 CA 7 1
= = , = = , = =
DE 10 2 EF 12 2 FD 14 2
1
The ratio of corresponding sides is .
2

Answers
1. a. congruent b. not congruent