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Exploring. 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.

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Presentation on theme: "Exploring. 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."— Presentation transcript:

1 Exploring

2 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.

3 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 = 5 2 + 6 2 = 9 2 = 25 + 36= 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.

4 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 = 11 2 + 60 2 = 61 2 = 121 + 3600= 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.

5 Classwork Page: 43-45 #3,5,6ab,8-10,12-14


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