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EXAMPLE 3

a = 10, b = 12, c = 16. a. a = 6, b = 8, c = 10. b. a 2 + b 2 c 2. a 2 + b 2 c 2. 6 2 + 8 2 10 2. 10 2 + 12 2 16 2. 100 + 144 256. 36 + 64 100. 100 = 100. 244 = 256. ?. ?. ?. ?. ?. ?. =. =. =. =. =. =. ANSWER. ANSWER.

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EXAMPLE 3

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  1. a = 10, b = 12, c = 16 a. a = 6, b = 8, c = 10 b. a 2 + b 2c 2 a 2 + b 2c 2 62 + 82 102 102 + 122 162 100 + 144 256 36 + 64 100 100 = 100 244 = 256 ? ? ? ? ? ? = = = = = = ANSWER ANSWER A right triangle Not a right triangle EXAMPLE 3 Identifying Right Triangles Use the converse of the Pythagorean Theorem to determine whether a triangle with the given side lengths is a right triangle.

  2. 5. Is a triangle with side lengths 14, 17, and 23 a right triangle? Explain. 142 + 172 232 ? = 485 = 529 ANSWER Not a right triangle for Example 3 GUIDED PRACTICE

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