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5.7 The Pythagorean Theorem

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a 2 + b 2 = c 2 The Pythagorean Theorem

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Examples: 1) Find the value of x. Give your answer in simplest radical form.

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Examples: 2) Find the value of x. Give your answer in simplest radical form.

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Examples: 3) Find the value of x. Give your answer in simplest radical form.

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Examples: 4) Find the value of x. Give your answer in simplest radical form.

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Examples: 5) Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter.

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Examples: 6) According to the recommended safety ratio of 4:1, how high will a 30-foot ladder reach when placed against a wall? Round to the nearest inch.

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Pythagorean Triple: A set of three nonzero whole numbers a, b, and c, such that a 2 + b 2 = c 2

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Examples: 7) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 7) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 8) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 9) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 10) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 11) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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Examples: 12) Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

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The Converse: If c 2 = a 2 + b 2, then the triangle is right. If, then the triangle is obtuse. If, then the triangle is acute. Also, in order for a figure to be a triangle, 2 sides must be greater than the third side.

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Examples: 13) Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10

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Examples: 14) Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 8, 17

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Examples: 15) Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 7, 12, 16

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Examples: 16) Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 11, 18, 34

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Examples: 17) Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 3.8, 4.1, 5.2