4 8 The Pythagorean Theorem Warm Up 2

4 -8 The Pythagorean Theorem Learn to use the Pythagorean Theorem and its converse

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

4 -8 The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos.

4 -8 The Pythagorean Theorem Directions: Find the leg of the hypotenuse to the

4 -8 The Pythagorean Theorem Example 1 Find the length of each leg first.

4 -8 The Pythagorean Theorem Example 2 c 4 5 a 2 + b

4 -8 The Pythagorean Theorem Example 3 c 5 7 a 2 + b

4 -8 The Pythagorean Theorem Example 4 25 7 a 2 + b 2

4 -8 The Pythagorean Theorem Example 5 12 b 4 a 2 + b

4 -8 The Pythagorean Theorem Directions: Determine whether or not the given numbers are

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

4 -8 The Pythagorean Theorem Example 7 Course 3

4 -8 The Pythagorean Theorem Lesson Summary Use the figure for Problems 1 and

Slides: 15

Download presentation

4 -8 The Pythagorean Theorem Warm Up 2 -16 -09 Estimate the value of each to the nearest tenth. 1. √ 30 5. 4 or 5. 5 2. √ 14 3. 7 or 3. 8 3. √ 55 7. 4 or 7. 5 4. √ 48 6. 9 Course 3

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

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

4 -8 The Pythagorean Theorem Course 3

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

4 -8 The Pythagorean Theorem Example 1 Find the length of each leg first. a 2 + b 2 = c 2 92 + 122 = c 2 81 + 144 = c 2 225 = c 15 = c Course 3 Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

4 -8 The Pythagorean Theorem Example 2 c 4 5 a 2 + b 2 = c 2 42 + 5 2 = c 2 16 + 25 = c 2 41 = c 6. 4 c Course 3 Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

4 -8 The Pythagorean Theorem Example 3 c 5 7 a 2 + b 2 = c 2 52 + 7 2 = c 2 25 + 49 = c 2 74 = c 8. 6 c Course 3 Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

4 -8 The Pythagorean Theorem Example 4 25 7 a 2 + b 2 = c 2 b 72 + b 2 = 252 49 + b 2 = 625 – 49 b 2 = 576 b = 24 Course 3 Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 49 from each side. Find the positive square root

4 -8 The Pythagorean Theorem Example 5 12 b 4 a 2 + b 2 = c 2 42 + b 2 = 122 16 + b 2 = 144 – 16 b 2 = 128 b 11. 3 Course 3 Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 16 from both sides. Find the positive square root.

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

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

4 -8 The Pythagorean Theorem Example 7 Course 3

4 -8 The Pythagorean Theorem Lesson Summary Use the figure for Problems 1 and 2. 1. Find the height h of the triangle. 8 m 2. Find the length of side c to the nearest meter. 12 m 3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers? 2624 ≈ 51 ft Course 3 c 10 m h 6 m 9 m

Related presentations