1. The
Pythagorean
Theorem c a b

2. All right triangles contain a right angle that measures 90.
The little square in the angle tells you it is a right angle.
90o

3. The two sides which form the right angle are called

4. The two sides which form the right angle are called

5. The two sides which form the right angle are called
legs.
The legs are labeled a and b. a b

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

7. And the length of the hypotenuse is usually labeled c.
It will be the longest side of the triangle. c a b

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

9. Pythagorus realized that if you have a right triangle,
and you square the lengths of the two sides that make the right angle, 3 4 5

10. you get the same number you would get by squaring the other side.
and add them together,  + 52 3 4 5
you get the same number you would get by squaring the other side.

11. 25 = 25 Is Pythagorus correct?
Yes, he is correct and it is true of any right triangle.

12. The relationship Pythagorus discovered about right triangles is now called The Pythagorean Theorem:
a2 + b2 = c2 b

13. Ex. 1 Suppose you drive directly west for 48 miles,
Then turn south and drive for 36 miles. 36 ?
How far have you traveled?

14. We can calculate the distance using the Pythagorean Theorem by ,48
482 +
362 = c2 36 c
because the route has formed a right triangle.

15. 48 36 c Which sides are the legs? 48 and 36
Which side is the hypotenuse? c

16. Then all we need to do is calculate:

17. So, since c2 is 3600, c is 60
you end up 60 miles from where you started. 48 36 60

18. Ex. # 2 Find the length of a diagonal of the rectangle:
15 8 ?

19. Find the length of a diagonal of the rectangle:
15
8  ?
b = 8 c
a = 15

20. 289 = c2
b = 8
a = 15 c

21. The length of the diagonal of the rectangle is
15"
8" 17

22. 5 12 c
# 3
= 13

23. = 24 10 b 26 #4
(a)
(c)

24. #5 12 b 15
= 9