Pythagorean Theorem Lesson

1. Tuesday 03/29

2. Name ____________________________ Warm-Up Date _____________________________ Pythagorean Theorem a2 + b2 = c2 ____ 8 cm 15 cm Label the legs and hypotenuse on the triangle above. Using the measurements above apply the Pythagorean Theorem to solve for the missing side. a2 + b2 = c2 82 + 152 = c2 Missing side = ______

3. Jacks parents bought a new washer and dryer, and he wants to help his father set up a ramp to get them in to the house. The deck that leads into the back door is 3 feet high and the sidewalk ends 4 feet from where the deck starts. How long does the ramp need to be? Can you create a quick drawing to model this situation?

4. Jacks parents bought a new washer and dryer, and he wants to help his father set up a ramp to get them in to the house. The deck that leads into the back door is 3 feet high and the sidewalk ends 4 feet from where the deck starts. How long does the ramp need to be? Now, can you use your tiles to model it this situation?

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9. Define, Postulates & Theorems Sides of a Right Triangle c The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. a Facts: Legs a and b are interchangeable. b

10. Define, Postulates & Theorems Sides of a Right Triangle Leg c The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. a Facts: Legs a and b are interchangeable. b

11. Define, Postulates & Theorems Sides of a Right Triangle Leg c The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. a Facts: Legs a and b are interchangeable. b Leg

12. Define, Postulates & Theorems Sides of a Right Triangle Hypotenuse Leg c The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. a Facts: Legs a and b are interchangeable. b Leg

13. Define, Postulates & Theorems Sides of a Right Triangle Hypotenuse Leg The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. c Opposite a Facts: Legs a and b are interchangeable. b Leg

14. Define, Postulates & Theorems Sides of a Right Triangle Hypotenuse Leg The Hypotenuse is the side_____________ the right angle. The Hypotenuse is the ___________ side to the right triangle. c Opposite a Facts: Legs a and b are interchangeable. b Longest Leg

15. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ _____ + _____= ______

16. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 3 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ 4 By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ _____ + _____= ______

17. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 9 3 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ 4 By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ _____ + _____= ______

18. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 9 3 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ 4 16 By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ _____ + _____= ______

19. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 9 3 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ 4 16 By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ _____ + _____= ______ 25

20. Investigate the Pythagorean Theorem Find the area of each square with side lengths of the right triangle. c2 c a a2 a b b b2 b2 9 3 Compare the area of the “leg squares” with the area of the “hypotenuse square” to complete the Pythagorean Theorem. a = ______ a2 = ______ b = ______ b2 = ______ 4 16 By rotating the square with the hypotenuse side lengths its area can be determined. c2 = ______ a2 b2 c2 _____ + _____= ______ 25

21. Formula: a2 + b2 = c2 Substitute values: into a, b, and c Solve: Get x by itself. (equations)

22. Let’s try these Formula: a2 + b2 = c2 x 13in. 8in.

23. Let’s try these Formula: a2 + b2 = c2 Substitute values: 132 + 82 = x2 x 8in. 13in.

24. Let’s try these Formula: a2 + b2 = c2 Substitute values: 132 + 82 = x2 x Solve:132 + 82 = x2 169 + 64 = x2 233 = x2 15.26 = x 8in. 13in.

25. Formula: a2 + b2 = c2 Let’s try these x 15in. 9in.

26. Formula: a2 + b2 = c2 Let’s try these Substitute values: x2 + 92 = 152 x 15in. 9in.

27. Formula: a2 + b2 = c2 Let’s try these Substitute values: x2 + 92 = 152 Solve:x2 + 92 = 152 x2 + 81 = 225 - 81 -81 x2 = 144 x = 12 x 15in. 9in.

28. Let’s try these Formula: a2 + b2 = c2 35in. 21in. x

29. Let’s try these Formula: a2 + b2 = c2 x2 + 212 = 352 Substitute values 35in. 21in. x

30. Let’s try these Formula: a2 + b2 = c2 Substitute values: x2 + 212 = 352 35in. 21in. Solve:x2 + 212 = 352 x2 + 441 = 1225 -441 -441 x2 = 784 x = 28 x

31. Let’s practice some basic problems.

32. Let’s practice some basic problems. 5 cm 5 cm ?

33. Let’s practice some basic problems. 5 cm. 5 cm. a2 + b2 = c2 52 + 52 = c2 50 = c2 c = ⎷50 cm ?

34. Let’s practice some basic problems. ? 14 ft 13 ft

35. Let’s practice some basic problems. a2 + b2 = c2 142 + 132 = c2 196+169 = c2 365 = c2 c = ⎷365 ft ? 14 ft 13 ft

36. Let’s practice some basic problems. ? 3 cm. 8 cm.

37. Let’s practice some basic problems. ? a2 + b2 = c2 x2 + 32 = 82 x2 + 9 = 64 -9 x2 =55 x =⎷55 3 cm. 8 cm.

38. Let’s practice some basic problems. ? 45 cm. 50 cm.

39. Let’s practice some basic problems. 18 ft. 12 ft.. ?

40. Let’s practice some basic problems. 45 in. ? 50 in.

41. . Practice - Pythagorean Theorem

42. . Answers to Practice

43. . Practice - Pythagorean Theorem

44. . Answers to Practice

45. Practice - Pythagorean Theorem

46. . Answers to Practice

47. . Practice - Pythagorean Theorem

48. . Answers to Practice