1. Applying the Pythagorean Theorem and Its Converse Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Applying the Pythagorean Theorem and Its Converse Warm Up Find the distance between each pair of points. 1. (8, 2) and (8, 7) ‏ 2. (–2, 4) and (5, 4) ‏ 3. (–1, –1) and (9, –1) ‏ 4. (–8, –4) and (–2, –4) ‏ 5 units 7 units 10 units 6 units

3. Applying the Pythagorean Theorem and Its Converse Problem of the Day The sum of the squares of two positive numbers is 100. One number is two more than the other. What are the numbers? 6 and 8

4. Applying the Pythagorean Theorem and Its Converse Learn to use the Distance Formula and the Pythagorean Theorem and its converse to solve problems.

5. Applying the Pythagorean Theorem and Its Converse 7.615  c Use the Pythagorean Theorem Simplify. 7 2 + 3 2 = c 2 49 + 9 = c 2 58 = c 2 58 = c Add. Additional Example 1: Marketing Application What is the diagonal length of the projector screen? The diagonal length should be given as about 7.62 feet.

6. Applying the Pythagorean Theorem and Its Converse 14.42  c Use the Pythagorean Theorem Simplify. 12 2 + 8 2 = c 2 144 + 64 = c 2 208 = c 2 208 = c Add. Check It Out: Example 1 What is the diagonal length of the projector screen? The diagonal length should be given as about 14.4 feet. 12 ft 8 ft

7. Applying the Pythagorean Theorem and Its Converse

8. Use the Distance Formula. J and K Additional Example 2A: Finding Distance on the Coordinate Plane Find the distances between the points to the nearest tenth. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

9. Applying the Pythagorean Theorem and Its Converse Substitute. Subtract. Additional Example 2A Continued Find the distances between the points to the nearest tenth. d = (0 – (–4))² + (–3 – 0 )² d = (4)² + (–3)² Simplify powers. d = 16 + 9 The distance between A and B is 5 units.

10. Applying the Pythagorean Theorem and Its Converse L and M Additional Example 2B: Finding Distance on the Coordinate Plane Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

11. Applying the Pythagorean Theorem and Its Converse Substitute. Subtract. Additional Example 2B Continued Find the distances between the points to the nearest tenth. d = (5 – 4)² + (–3 – 0)² d = (1)² + (–3)² Simplify powers. d = 1 + 9 The distance between L and M is about 3.2 units.

12. Applying the Pythagorean Theorem and Its Converse J and L Check It Out: Example 2A Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

13. Applying the Pythagorean Theorem and Its Converse Substitute. Subtract. Check It Out: Example 2A Continued Find the distances between the points to the nearest tenth. d = (4 – (–4))² + (0 – 0)² d = (8)² + (0)² Simplify powers. d = 64 + 0 The distance between J and L is 8 units.

14. Applying the Pythagorean Theorem and Its Converse K and M Check It Out: Example 2B Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

15. Applying the Pythagorean Theorem and Its Converse Substitute. Subtract. Check It Out: Example 2B Continued Find the distances between the points to the nearest tenth. d = ((–4) – 0)² + (– 3 – (–3)² d = (–4)² + (0)² Simplify powers. d = 16 + 0 The distance between K and M is 4 units.

16. Applying the Pythagorean Theorem and Its Converse Additional Example 3A: Identifying a Right Triangle a 2 + b 2 = c 2 9 2 + 12 2 = 15 2 81 + 144 = 225 225 = 225 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. Tell whether the given side lengths form a right triangle. 9, 12, 15 Simplify. Add.

17. Applying the Pythagorean Theorem and Its Converse Additional Example 3B: Identifying a Right Triangle a 2 + b 2 = c 2 8 2 + 10 2 = 13 2 63 + 100 = 169 163 ≠ 169 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. Tell whether the given side lengths form a right triangle. 8, 10, 13 Simplify. Add.

18. Applying the Pythagorean Theorem and Its Converse Check It Out: Example 3A a 2 + b 2 = c 2 5 2 + 6 2 = 9 2 25 + 36 = 81 61 ≠ 81 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. Tell whether the given side lengths form a right triangle. 5, 6, 9 Simplify. Add.

19. Applying the Pythagorean Theorem and Its Converse Check It Out: Example 3B a 2 + b 2 = c 2 8 2 + 15 2 = 17 2 64 + 225 = 289 289 = 289 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. Tell whether the given side lengths form a right triangle. 8, 15, 17 Simplify. Add.