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 Math Journal (5 Min) Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.

3. Applying the Pythagorean Theorem and Its Converse 3-9 Homework Review (5 Min)

4. 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

5. 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

6. Applying the Pythagorean Theorem and Its Converse 3-9 Textbook Examples (I Do) (5 Min)

7. 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.

8. 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. 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.

9. 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: 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

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

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

12. 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.

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

14. 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.

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

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

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

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

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

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

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

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

23. Applying the Pythagorean Theorem and Its Converse 3-9 Class work Problems (We Do) (10 Min) Pg. 140-141 (1-8)

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

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

26. Applying the Pythagorean Theorem and Its Converse 3-9 Small Group CW(Yall Do) (10 Min) Pg. 140-141 (10 – 38 EOE)

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

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

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

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

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

32. Applying the Pythagorean Theorem and Its Converse 3-9 Homework (You Do) (10 Min) Pg. 114-115 (15, 23, 27, 31, 39, odd)

33. Applying the Pythagorean Theorem and Its Converse 3-9 Math Journal (5 Min) Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.

34. Applying the Pythagorean Theorem and Its Converse 3-9 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

35. 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.

36. 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.

37. 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.

38. Applying the Pythagorean Theorem and Its Converse 3-9 1. Find the length of the diagonal of the rectangle. width = 5 m, length = 12 m A. 8 m B. 11 m C. 13 m D. 17 m Lesson Quiz for Student Response Systems

39. Applying the Pythagorean Theorem and Its Converse 3-9 2. Find the distance between the points to the nearest tenth. Q and S A. 6.0 m B. 6.1 m C. 7.0 m D. 37.1 m Lesson Quiz for Student Response Systems

40. Applying the Pythagorean Theorem and Its Converse 3-9 3. Tell whether the given side lengths form a right triangle. 12 ft, 13 ft, 14 ft A. yes B. no Lesson Quiz for Student Response Systems