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Unit 1: Square Roots & The Pythagorean Theorem 1.6 Exploring the Pythagorean Theorem Math 8 MacLean The Pythagorean Theorem is true for right triangles only! To see which triangle is a right triangle, check to see if the area of the square on the longest side is equal to the sum of the areas of the squares on the other two sides. A = 225 cm2 A = 169 cm2 15 cm 13 cm 12 cm 7 cm P Q 5 cm A = 144 cm2 A = 49 cm2 10 cm A = 100 cm2 A = 25 cm2 a2 + b2 = c2 52 + 122 = 132 25 + 144 = 169 a2 + b2 = c2 72 + 102 = 152 49 + 100 ≠ 25 The Pythagorean Theorem applies to the triangle P, but not to triangle Q. A set of three whole numbers that satisfy the Pythagorean Theorem is called a Pythagorean triple. For example, the number combination 5 – 12 - 13 is a Pythagorean triple because 52 + 122 = 132 and they are all whole numbers! Try These: 1. Is this triangle a right triangle? Show your work to prove your answer. 13 cm 10 cm 8 cm 𝑎2 + 𝑏 2 = 𝑐 2 82 + 102 = 132 64 + 100 = 169 164 ≠ 169 No, it is not a right triangle. It does not satisfy the Pythagorean Theorem. 2. Is a triangle with side lengths 5, 12, and 13 cm a right triangle? Is it a Pythagorean Triple? Explain. 𝑎2 + 𝑏 2 = 𝑐 2 52 + 122 = 132 25 + 144 = 169 169 = 169 Yes, it is a right triangle. It satisfies the Pythagorean Theorem. It is also a Pythagorean Triple because it is three whole numbers.