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SOLUTION

AB. 4. 8. Is either DEF or GHJ similar to ABC ?. DE. 3. 6. Compare ABC and DEF by finding ratios of corresponding side lengths. =. =. EXAMPLE 1. Use the SSS Similarity Theorem. SOLUTION. Shortest sides. =. =. =. =. 12. 4. BC. 8. 16. 4. CA. AB. 12.

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SOLUTION

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  1. 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

  2. = = = = 12 4 BC 8 16 4 CA AB 12 8 9 3 FD EF GH 3 All of the ratios are equal, so ABC~DEF. ANSWER 1 = = EXAMPLE 1 Use the SSS Similarity Theorem Longest sides Remaining sides Compare ABCand GHJby finding ratios of corresponding side lengths. Shortest sides

  3. 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

  4. 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.

  5. 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

  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

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

  8. 20 = = ST 33 LM 5 24 6 LN 24 RS Compare MLNand RSTby finding ratios of corresponding side lengths. = LN 36 13 = = RT 30 15 The ratios are not all equal, so LMN and RSTare not similar. for Examples 1 and 2 GUIDED PRACTICE SOLUTION Shortest sides Longest sides Remaining sides

  9. 20 = = = 26 LN LM 2 2 30 39 XZ 3 3 YZ Compare LMNand ZYXby finding ratios of corresponding side lengths. = MN 24 2 = = XZ 36 3 ANSWER All of the ratios are equal, so MLN ~ZYX. for Examples 1 and 2 GUIDED PRACTICE Shortest sides Longest sides Remaining sides

  10. 12 A B y x C 2. The shortest side of a triangle similar to RSTis 12 units long. Find the other side lengths of the triangle. 30 24 = x 12 24x= 12 30 for Examples 1 and 2 GUIDED PRACTICE Find the value of xthat makes corresponding side lengths proportional. Write proportion. Cross Products Property x= 15

  11. 33 24 = y 12 24y = 12 33 ANSWER So x = AC = 15and y = BC = 16.5 for Examples 1 and 2 GUIDED PRACTICE Again to find out y Write proportion. Cross Products Property y = 16.5

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