1. Sec 6.6 Pythagorean Theorem

2. Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite to the right angle

3. Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! Leg leg hypotenuse

4. Leg 2 Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! hypotenuse Leg 1

5. Leg 2 Hyp Pythagorean Theorem Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! (Leg1) 2 + (leg2) 2 = (Hyp) 2

6. 6 8 x Solve for x. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

7. 4 7 y Solve for y. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

8. 6 t 15 Solve for t. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

9. Pythagorean Triples 3 4 5 6 8 10 9 12 15 12 16 20

10. Pythagorean Triples 3 4 5 6 8 10 9 12 15 12 16 20 5 12 13 10 24 26 15 36 39 7 24 25 14 48 50 21 72 75 9 15 12

11. To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet. 4 ft. 10 ft. x (Leg1) 2 + (leg2) 2 = (Hyp) 2

12. 20 miles A car drives 20 miles due east and then 45 miles due south. To the nearest hundredth of a mile, how far is the car from its starting point? 45 miles x

13. Application The Pythagorean theorem has far-reaching ramifications in other fields (such as the arts), as well as practical applications. The theorem is invaluable when computing distances between two points, such as in navigation and land surveying. Another important application is in the design of ramps. Ramp designs for handicap-accessible sites and for skateboard parks are very much in demand.

14. Wall Ladder HYP Leg 1 Leg 2

15. Informal Proof #1 Inscribe a square within the square.

16. a b a a a b b b c c c c Informal Proof #1

17. a b a a a b b b c c c c a b c

18. b a a a b b c c c a b c

19. b a a a b b c c c a b c a b c

20. b a a b c c a b c a b c

21. b a a b c c a b c a b c b a c

22. a b c a b c a b c b a c

23. a b c a b c a b c b a c a b c

24. a b c a b c b a c a b c

25. a b c a b c b a c a b c

26. a b c a b c b a c a b c a b c

27. a b c b a c a b c a b c a b c

28. b a c a b c a b c a b c a b c

29. b a c a b c a b c a b c b a c

30. a b c a b c a b c b a c

31. a b a a a b b b c c c c Informal Proof #2 a + b Total Purple Yellow Area Area Area - = - =