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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.

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Presentation on theme: "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."— Presentation transcript:

1 Course The Pythagorean Theorem Warm Up Estimate the value of each to the nearest tenth. 1. √ √14 3. √55 4. √ or or or

2 Course The Pythagorean Theorem Learn to use the Pythagorean Theorem and its converse to solve problems. Course 3 The Pythagorean Theorem

3 Course The Pythagorean Theorem Pythagorean Theorem leg hypotenuse Vocabulary

4 Course 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.

5 Course The Pythagorean Theorem

6 Course The Pythagorean Theorem Directions: Find the leg of the hypotenuse to the nearest tenth.

7 Course The Pythagorean Theorem 15 = c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c = c = c = c Simplify powers. Solve for c; c = c 2. Example 1 Find the length of each leg first.

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

9 Course The Pythagorean Theorem Example c 8.6  c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c = c = c 2 74 = c Simplify powers. Solve for c; c = c 2.

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

11 Course The Pythagorean Theorem Example 5 b  b a 2 + b 2 = c b 2 = 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.

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

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

14 Course The Pythagorean Theorem Example 7

15 Course 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 ≈ 51 ft


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