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Pythagorean Theorem For any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Note: The hypotenuse is always the longest side of a right triangle. We can verify if a triangle is a right triangle by checking if this equation is satisfied.

The Pythagorean Theorem Example 1: Determine whether a triangle with side lengths 5 cm, 9 cm, and 6 cm is a right triangle. c = longest side = 9 cma and b = legs = 5 cm and 6 cm a 2 + b 2 c 2 = = 9 2 = = 81 = 61= 81 Since 61 ≠ 81, the Pythagorean theorem is not satisfied, so the triangle is not a right triangle. If it were a right triangle, then a 2 + b 2 would give the same number as c 2.

The Pythagorean Theorem Example 2: Determine whether a triangle with side lengths 11, 61, 60 is a right triangle. c = longest side = 61 cma and b = legs = 11 cm and 60 cm a 2 + b 2 c 2 = = 61 2 = = 3721= 3721 Since 3721 = 3721, the Pythagorean theorem is satisfied, so the triangle is a right triangle. A set of three whole numbers that satisfies the Pythagorean Theorem is called a Pythagorean triple.

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