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Course 3 4-8 The Pythagorean Theorem Warm Up2-16-09 Estimate the value of each to the nearest tenth. 1. √ 30 2. √14 3. √55 4. √48 5.4 or 5.5 3.7 or 3.8 7.4 or 7.5 6.9

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Course 3 4-8 The Pythagorean Theorem Learn to use the Pythagorean Theorem and its converse to solve problems. Course 3 The Pythagorean Theorem

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Course 3 4-8 The Pythagorean Theorem Pythagorean Theorem leg hypotenuse Vocabulary

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Course 3 4-8 The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

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Course 3 4-8 The Pythagorean Theorem

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Course 3 4-8 The Pythagorean Theorem Directions: Find the leg of the hypotenuse to the nearest tenth.

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Course 3 4-8 The Pythagorean Theorem 15 = c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c 2 9 2 + 12 2 = c 2 81 + 144 = c 2 225 = c Simplify powers. Solve for c; c = c 2. Example 1 Find the length of each leg first.

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Course 3 4-8 The Pythagorean Theorem 4 5 c 6.4 c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c 2 4 2 + 5 2 = c 2 16 + 25 = c 2 41 = c Simplify powers. Solve for c; c = c 2. Example 2 41 = c 2

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Course 3 4-8 The Pythagorean Theorem Example 3 5 7 c 8.6 c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c 2 5 2 + 7 2 = c 2 25 + 49 = c 2 74 = c Simplify powers. Solve for c; c = c 2.

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Course 3 4-8 The Pythagorean Theorem Example 4 25 7 b Find the positive square root b = 24 a 2 + b 2 = c 2 7 2 + b 2 = 25 2 49 + b 2 = 625 –49 b 2 = 576 Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 49 from each side.

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Course 3 4-8 The Pythagorean Theorem Example 5 b 11.3 12 4 b a 2 + b 2 = c 2 4 2 + b 2 = 12 2 16 + b 2 = 144 –16 b 2 = 128 Find the positive square root. Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 16 from both sides.

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Course 3 4-8 The Pythagorean Theorem Directions: Determine whether or not the given numbers are possible measures for the sides of a right triangle.

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Course 3 4-8 The Pythagorean Theorem Example 6 a = 3, b=4 and c = 5

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Course 3 4-8 The Pythagorean Theorem Example 7

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Course 3 4-8 The Pythagorean Theorem Lesson Summary 1. Find the height h of the triangle. 2. Find the length of side c to the nearest meter. 3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers? 8 m 12 m h c 10 m 6 m9 m Use the figure for Problems 1 and 2. 2624 ≈ 51 ft

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