Sec 6.6 Pythagorean Theorem

1. Sec 6.6 Pythagorean Theorem (Leg1)2 + (leg2)2 = (Hyp)2 hypotenuse Leg 1 Leg 2

2. Objective- To find the missing side of a right triangle by using Pythagorean Theorem. For Right Triangles Only! - always opposite to the right angle hypotenuse leg leg

3. Objective- To find the missing side of a right triangles by using Pythagorean Theorem. For Right Triangles Only! hypotenuse Leg leg

4. Objective- To find the missing side of a right triangles by using Pythagorean Theorem. For Right Triangles Only! hypotenuse Leg 1 Leg 2

5. Objective- To find the missing side of a right triangles by using Pythagorean Theorem. For Right Triangles Only! Pythagorean Theorem Hyp Leg 1 (Leg1)2 + (leg2)2 = (Hyp)2 Leg 2

6. Solve for x. (Leg1)2 + (leg2)2 = (Hyp)2 x 6 (Hyp) (Leg 1) 8 (Leg 2) Line Segment can’t be negative.

7. Solve for y. (Leg1)2 + (leg2)2 = (Hyp)2 7 (Leg 2) 4 y (Leg 1) (Hyp) Line Segment can’t be negative.

8. Solve for t. (Leg1)2 + (leg2)2 = (Hyp)2 6 (Leg 1) t 15 (Leg 2) (Hyp) Line Segment can’t be negative.

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

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

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. (Leg1)2 + (leg2)2 = (Hyp)2 x 4 ft. 10 ft.

12. 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? 20 miles x 45 miles

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. Steps of Solving Pythagorean Word Problems 1. Draw and Label the diagram. (Leg 1, Leg 2 and Hypotenuse) 2. Write out (Leg 1)2 + (leg 2)2 = (Hyp)2 3. Set up the equation. 4. Solve for the unknown. 5. Write a conclusion statement.

15. (Leg1)2 + (leg2)2 = (Hyp)2 #1 & #3 Diagram: Ladder Wall HYP Leg 1 Leg 2

16. Soccer Field Diagram #2 (Leg1)2 + (leg2)2 = (Hyp)2 Leg 2 = 90 Leg 1 = 120

17. Rectangle & Diagonal (#4 & #5) (Leg 2 = __) Hyp = ___ (Leg 1 = __) Width = Leg Diagonal = Hypotenuse Lenth = Leg

18. #8

19. Square vs. Diagonal (Ex. Baseball Diamond) Second HOME

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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