1. Applying the Pythagorean Theorem and Its Converse 3-9 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 3-9 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 3-9 Learn to use the Distance Formula and the Pythagorean Theorem and its converse to solve problems.

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

5. Applying the Pythagorean Theorem and Its Converse 3-9 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 B. What is the diagonal length of the projector screen? The diagonal length should be given as about 14.4 feet. 12 ft 8 ft

6. Applying the Pythagorean Theorem and Its Converse 3-9

7. Applying the Pythagorean Theorem and Its Converse 3-9 Use the Distance Formula. J and K Example 2: Finding Distance on the Coordinate Plane A. 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.

8. Applying the Pythagorean Theorem and Its Converse 3-9 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.

9. Applying the Pythagorean Theorem and Its Converse 3-9 L and M Example 2: Finding Distance on the Coordinate Plane B. 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.

10. Applying the Pythagorean Theorem and Its Converse 3-9 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.

11. Applying the Pythagorean Theorem and Its Converse 3-9 J and L Check It Out C. 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.

12. Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example 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.

13. Applying the Pythagorean Theorem and Its Converse 3-9 K and M Check It Out D. 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.

14. Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example D 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.

15. Applying the Pythagorean Theorem and Its Converse 3-9 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

16. Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: 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. A. Tell whether the given side lengths form a right triangle. 9, 12, 15 Simplify. Add.

17. Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: 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. B. Tell whether the given side lengths form a right triangle. 8, 10, 13 Simplify. Add.

18. Applying the Pythagorean Theorem and Its Converse 3-9 Check It Out 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. C. Tell whether the given side lengths form a right triangle. 5, 6, 9 Simplify. Add.

19. Applying the Pythagorean Theorem and Its Converse 3-9 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. D. Tell whether the given side lengths form a right triangle. 8, 15, 17 Simplify. Add.

20. Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz

21. Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part I 1. width = 9 in., length = 40 in. 2. base length = 20 m, height = 15 m. 41 in. 25 m Find the length of the diagonal of the rectangle.

22. Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part II 3. Q and R 4. S and T ≈ 6.3 ≈ 2.2 Find the distance between the points to the nearest tenth.

23. Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part III 5. 12 cm, 13 cm, 16 cm 6. 11 ft, 60 ft, 61 ft no yes Tell whether the given side lengths form a right triangle.