1. 6-3 The Pythagorean Theorem Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Graph the figures with the given verticals and find the area. 1. (–1, –1), (–1, 3), (6, –1) 2. (2, 1), (8, 1), (6, –3) 3. (3, –2), (15, –2), (14, 6), (4, 6) Course 3 6-3 The Pythagorean Theorem 14 units 2 12 units 2 88 units 2

3. Problem of the Day A side of a square A is 5 times the length of square B. How many times as great is the area of square A than the area of square B? Course 3 6-3 The Pythagorean Theorem 25

4. Learn to use the Pythagorean Theorem and its converse to solve problems. Course 3 6-3 The Pythagorean Theorem

5. Course 3 6-3 The Pythagorean Theorem Pythagorean Theorem leg hypotenuse Vocabulary

6. Course 3 6-3 The Pythagorean Theorem a 2 + b 2 = c 2

7. Course 3 6-3 The Pythagorean Theorem 4 5 c 6.40  c A. 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. Additional Example 1A: Find the the Length of a Hypotenuse Find the length of the hypotenuse. 41 = c 2

8. Course 3 6-3 The Pythagorean Theorem 15 = c B. 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. Additional Example 1B: Find the the Length of a Hypotenuse Find the length of the hypotenuse. triangle with coordinates (1, –2), (1, 7), and (13, –2)

9. Course 3 6-3 The Pythagorean Theorem Try This: Example 1A 5 7 c A. Find the length of the hypotenuse. 8.60  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.

10. Course 3 6-3 The Pythagorean Theorem B. triangle with coordinates (–2, –2), (–2, 4), and (3, –2) x y The points form a right triangle. (–2, –2) (–2, 4) (3, –2) Try This: Example 1B Find the length of the hypotenuse. 7.81  c Pythagorean Theorem a 2 + b 2 = c 2 6 2 + 5 2 = c 2 36 + 25 = c 2 61 = c Simplify powers. Solve for c; c = c 2. Substitute for a and b.

11. Course 3 6-3 The Pythagorean Theorem Additional Example: 2 Finding the Length of a Leg in a Right Triangle 25 7 b 576 = 24 b = 24 a 2 + b 2 = c 2 7 2 + b 2 = 25 2 49 + b 2 = 625 –49 b 2 = 576 Solve for the unknown side in the right triangle. Pythagorean Theorem Substitute for a and c. Simplify powers.

12. Course 3 6-3 The Pythagorean Theorem Try This: Example 2 b  11.31 12 4 b a 2 + b 2 = c 2 4 2 + b 2 = 12 2 16 + b 2 = 144 –16 b 2 = 128 128  11.31 Solve for the unknown side in the right triangle. Pythagorean Theorem Substitute for a and c. Simplify powers.

13. Course 3 6-3 The Pythagorean Theorem Additional Example 3: Using the Pythagorean Theorem to Find Area a 66 44 a 2 + b 2 = c 2 a 2 + 4 2 = 6 2 a 2 + 16 = 36 a 2 = 20 a = 20 units ≈ 4.47 units Find the square root of both sides. Substitute for b and c. Pythagorean Theorem A = hb = (8)( 20) = 4 20 units 2  17.89 units 2 1212 1212 Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle.

14. Course 3 6-3 The Pythagorean Theorem a 2 + b 2 = c 2 a 2 + 2 2 = 5 2 a 2 + 4 = 25 a 2 = 21 a = 21 units ≈ 4.58 units Find the square root of both sides. Substitute for b and c. Pythagorean Theorem A = hb = (4)( 21) = 2 21 units 2  4.58 units 2 1212 1212 Try This: Example 3 Use the Pythagorean Theorem to find the height of the triangle. Then use the height to find the area of the triangle. a 55 22

15. Course 3 6-3 The Pythagorean Theorem Lesson Quiz 1. Find the height of the triangle. 2. Find the length of side c to the nearest meter. 3. Find the area of the largest triangle. 4. One leg of a right triangle is 48 units long, and the hypotenuse is 50 units long. How long is the other leg? 8m 12m 60m 2 14 units h c 10 m 6 m9 m Use the figure for Problems 1-3.