SOLUTION

EXAMPLE 1 Use the SSS Similarity Theorem

Compare ABC and DEF by finding ratios of corresponding side lengths.

Shortest sidesABDE

43

86 ==

Is either DEF or GHJ similar to ABC?

EXAMPLE 1

Longest sides CAFD

43

1612 ==

Remaining sidesBCEF

43

12 9 ==

Compare ABC and GHJ by finding ratios of corresponding side lengths.

Shortest sides

Use the SSS Similarity Theorem

ABGH

88 == 1

All of the ratios are equal, so ABC ~ DEF.ANSWER

EXAMPLE 1 Use the SSS Similarity Theorem

Longest sides CAJG

1616 == 1

Remaining sides BCHJ

65

1210 ==

The ratios are not all equal, so ABC and GHJ are not similar.

ANSWER

SOLUTION

EXAMPLE 2 Use the SSS Similarity Theorem

ALGEBRA

Find the value of x that makes ABC ~ DEF.

STEP 1 Find the value of x that makes corresponding side lengths proportional.

412 = x –1

18 Write proportion.

EXAMPLE 2 Use the SSS Similarity Theorem

4 18 = 12(x – 1)

72 = 12x – 12

7 = x

Cross Products Property

Simplify.

Solve for x.

Check that the side lengths are proportional when x = 7.

STEP 2

BC = x – 1 = 6

618

412 =

ABDE

BCEF=?

EXAMPLE 2 Use the SSS Similarity Theorem

DF = 3(x + 1) = 24

824

412 =

ABDE

ACDF=?

When x = 7, the triangles are similar by the SSS Similarity Theorem.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

1. Which of the three triangles are similar? Write a similarity statement.

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

Compare MLN and RST by finding ratios of corresponding side lengths.

Shortest sides LM RS

56

2024 ==

Longest sides ST LN

3324=

Remaining sides LN RT

3630 = = 13

15

The ratios are not all equal, so LMN and RST are not similar.

GUIDED PRACTICE for Examples 1 and 2

Compare LMN and ZYX by finding ratios of corresponding side lengths.

Shortest sides

Remaining sides

Longest sides

LM YZ

23

2030 ==

23=LN

XZ 2639=

MN XZ

2436 = = 2

3

All of the ratios are equal, so MLN ~ ZYX.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

2. The shortest side of a triangle similar to RST is 12 units long. Find the other side lengths of the triangle.

A B

C

12

x y

Find the value of x that makes corresponding side lengths proportional.

2412

= 30 x

Write proportion.

x = 15

Cross Products Property24x = 12 30

GUIDED PRACTICE for Examples 1 and 2

Again to find out y

2412

= 33y

Write proportion.

y = 16.5

Cross Products Property24y = 12 33

So x = AC = 15 and y = BC = 16.5

ANSWER