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

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

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

ALGEBRA Find the value of xthat makes ABC ~ DEF. 4 x–1 12 18 STEP1 Find the value of xthat makes corresponding side lengths proportional. = EXAMPLE 2 Use the SSS Similarity Theorem SOLUTION Write proportion.

BC AB 6 4 STEP2 Check that the side lengths are proportional when x = 7. 4 18 = 12(x – 1) 12 18 EF DE ? = = EXAMPLE 2 Use the SSS Similarity Theorem Cross Products Property 72 = 12x – 12 Simplify. 7 = x Solve for x. BC = x – 1 = 6

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

1.Which of the three triangles are similar? Write a similarity statement. ANSWER MLN ~ZYX. for Examples 1 and 2 GUIDED PRACTICE

2. The shortest side of a triangle similar to RSTis 12 units long. Find the other side lengths of the triangle. 15, 16.5 ANSWER for Examples 1 and 2 GUIDED PRACTICE

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