2. This is a right triangle:

3. We call it a right triangle because it contains a right angle.

4. The measure of a right angle is 90 o 90 o

5. The little square 90 o in the angle tells you it is a right angle.

6. About 2,500 years ago, a Greek mathematician named Pythagoras discovered a special relationship between the sides of right triangles.

7. Pythagoras realized that if you have a right triangle, 3 4 5

8. and you square the lengths of the two sides that make up the right angle, 3 4 5

9. and add them together, 3 4 5

10. you get the same number you would get by squaring the other side. 3 4 5

11. Is that correct? ? ?

12. And it is true for any right triangle. 8 6 10 It is

13. The two sides which come together in a right angle are called

14. The lengths of the legs are usually called a and b. a b

15. The side across from the right angle is called the... a b

16. And the length of the hypotenuse is ALWAYS labeled c. a b c

17. The relationship Pythagoras discovered is now called The Pythagorean Theorem a b c

18. The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c, a b c

19. then a b c

20. You can use The Pythagorean Theorem to solve many kinds of problems. Suppose you drive directly west for 48 kms, 48

21. Then turn south and drive for 36 kms. 48 36

22. How far are you from where you started? (as the crow flies) 48 36 ?

23. 48 2 Using The Pythagorean Theorem, 48 36 c 36 2 +=c2c2

24. can you see that we have a right triangle? 48 36 c 48 2 36 2 +=c2c2

25. Which side is the hypotenuse? Which sides are the legs? 48 36 c 48 2 +36 2 c2c2 =

26. Then all we need to do is calculate:

27. And you end up 60 kms from where you started. 48 36 60 60. So, since c 2 is 3600, c is

28. Find the length of a diagonal of the rectangle: 15" 8" ?

29. 15" 8" ? b = 8 a = 15 c Remember, rectangles are really two triangles that are attached.

30. b = 8 a = 15 c

31. Practice using The Pythagorean Theorem to solve these right triangles:

32. 5 12 c = 13

33. 10 b = 26

34. 10 b 26 = 24 (a)(a) (c)(c) so... b = 24

35. 12 b 15 = 9

36. PRACTICE... Read text pages 25 thru 30. Work carefully through the examples. HOMEWORK: p. 30 & 31 (1 to 5 and then 1 to 3) - Show your work - Check your answers