EXAMPLE 1 Is either Use the SSS Similarity

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EXAMPLE 1 Is either Use the SSS Similarity Theorem DEF or GHJ similar to

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

EXAMPLE 1 Use the SSS Similarity Theorem Longest sides Remaining sides CA 16 4

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

EXAMPLE 1 Use the SSS Similarity Theorem Longest sides CA 16 1 JG =

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

EXAMPLE 2 Use the SSS Similarity Theorem ALGEBRA Find the value of x that

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 x – 1 = 12 18 Write proportion.

EXAMPLE 2 Use the SSS Similarity Theorem 4 18 = 12(x – 1) 72

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

EXAMPLE 2 Use the SSS Similarity Theorem DF = 3(x + 1) = 24

EXAMPLE 2 Use the SSS Similarity Theorem DF = 3(x + 1) = 24 AB ? AC DE = DF 8 4 12 = 24 ANSWER When x = 7, the triangles are similar by the SSS Similarity Theorem.

GUIDED PRACTICE 1. for Examples 1 and 2 Which of the three triangles are

GUIDED PRACTICE 1. for Examples 1 and 2 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

GUIDED PRACTICE for Examples 1 and 2 SOLUTION Compare MLN and RST by finding ratios of corresponding side lengths. LM 20 5 Shortest sides RS = 24 = 6 Longest sides ST = 33 LN 24 Remaining sides LN = 36 = 13 RT 30 15 The ratios are not all equal, so not similar. LMN and RST are

GUIDED PRACTICE for Examples 1 and 2 Compare LMN and ZYX by finding ratios

GUIDED PRACTICE for Examples 1 and 2 Compare LMN and ZYX by finding ratios of corresponding side lengths. LM 20 2 Shortest sides YZ = 30 = 3 Longest sides LN 26 2 = = XZ 39 3 Remaining sides MN = 24 = 2 XZ 36 3 ANSWER All of the ratios are equal, so MLN ~ ZYX.

GUIDED PRACTICE 2. for Examples 1 and 2 The shortest side of a triangle

GUIDED PRACTICE 2. for Examples 1 and 2 The shortest side of a triangle similar to RST is 12 units long. Find the other side lengths of the triangle. A 12 y x C Find the value of x that makes corresponding side lengths proportional. 24 = 30 x 12 24 x = 12 30 x = 15 B Write proportion. Cross Products Property

GUIDED PRACTICE for Examples 1 and 2 Again to find out y 24 =

GUIDED PRACTICE for Examples 1 and 2 Again to find out y 24 = 33 y 12 24 y = 12 33 Write proportion. Cross Products Property y = 16. 5 ANSWER So x = AC = 15 and y = BC = 16. 5

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