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EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c 2 = a 2 + b 2. 9 34 81 + 225 = ? = ? (3 34) 2 9 2 + 15 2 a. 306 = 306 b. 26 2 22 2 + 14 2 = ? 676 484 + 196 = ? 676 = 680 The triangle is a right triangle. The triangle is not a right triangle.
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GUIDED PRACTICE for Example 1 Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c 2 = a 2 + b 2. 64 = 64 The triangle is a right triangle. 1. 4 2 + = (4 3 ) 2 8282 64 = 16 + 16 3 4,4 3, 8 Tell whether a triangle with the given side lengths is a right triangle.
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GUIDED PRACTICE for Example 1 121 + 100 196 = 196 = 221 The triangle is not a right triangle. 2. 11 2 + 10 2 = 14 2 10, 11, and 14 c 2 = a 2 + b 2 Let c represent the length of the longest side of the triangle.Check to see whether the side lengths satisfy the equation Tell whether a triangle with the given side lengths is a right triangle.
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GUIDED PRACTICE for Example 1 The triangle is a right triangle. 3. ( 61) 2 5 2 + 6 2 = 61 25 + 36 = 61 = 61 c 2 = a 2 + b 2 5,6 and 61 Let c represent the length of the longest side of the triangle.Check to see whether the side lengths satisfy the equation Tell whether a triangle with the given side lengths is a right triangle.
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