EXAMPLE 1 Use the SSS Similarity Theorem Is either DEF or GHJ similar to ABC? SOLUTION Compare ABC and DEF by finding ratios of corresponding side lengths. Shortest sides AB DE 4 3 8 6 =

EXAMPLE 1 Use the SSS Similarity Theorem Longest sides CA FD 4 3 16 12 = Remaining sides BC EF 4 3 12 9 = All of the ratios are equal, so ABC ~ DEF. ANSWER Compare ABC and GHJ by finding ratios of corresponding side lengths. Shortest sides AB GH 8 = 1

EXAMPLE 1 Use the SSS Similarity Theorem Longest sides CA JG 16 = 1 Remaining sides BC HJ 6 5 12 10 = The ratios are not all equal, so ABC and GHJ are not similar. ANSWER

Use the SSS Similarity Theorem EXAMPLE 2 Use the SSS Similarity Theorem ALGEBRA Find the value of x that makes ABC ~ DEF. SOLUTION STEP 1 Find the value of x that makes corresponding side lengths proportional. 4 12 = x –1 18 Write proportion.

Use the SSS Similarity Theorem EXAMPLE 2 Use the SSS Similarity Theorem 4 18 = 12(x – 1) Cross Products Property 72 = 12x – 12 Simplify. 7 = x Solve for x. Check that the side lengths are proportional when x = 7. STEP 2 BC = x – 1 = 6 AB DE BC EF = ? 6 18 4 12 =

Use the SSS Similarity Theorem EXAMPLE 2 Use the SSS Similarity Theorem DF = 3(x + 1) = 24 AB DE AC DF = ? 8 24 4 12 = 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. LM RS 5 6 20 24 = Shortest sides ST LN 33 24 = Longest sides LN RT 36 30 = 13 15 Remaining sides 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. LM YZ 2 3 20 30 = Shortest sides 2 3 = LN XZ 26 39 Longest sides MN XZ 24 36 = 2 3 Remaining sides 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. 24 12 = 30 x Write proportion. 24x = 12 30 Cross Products Property x = 15

GUIDED PRACTICE for Examples 1 and 2 Again to find out y 24 33 = 12 y Write proportion. 24y = 12 33 Cross Products Property y = 16.5 So x = AC = 15 and y = BC = 16.5 ANSWER