1. The Pythagorean Theorem x z y

3. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c

4. The Pythagorean Theorem Copy the triangle three more times and build a square with each triangle at a corner a b c

5. The Pythagorean Theorem Copy the labels to the corresponding sides a b c a a a b b b c c c

6. The Pythagorean Theorem a b c a a a b b b c c c The Area of the big square can be found by multiplying the lengths of the sides (a + b)(a + b)

7. The Pythagorean Theorem a b c a a a b b b c c c

8. a b c a a b b c c c

10. a b c

11. Example 1 For this example we will be given both legs and will be trying to find the hypotenuse 10 x 6

12. Example 1 Setup the equation using the Pythagorean Theorem: (Small leg) 2 + (Large leg) 2 = hypotenuse 2 10 x 6

13. Example 1

14. Example 2 For this example we will be given a leg and the hypotenuse and will be trying to find the other leg 9 x 4

15. Example 2 9 x 4 Setup the equation using the Pythagorean Theorem: (Small leg) 2 + (Large leg) 2 = hypotenuse 2 4 2 + x 2 = 9 2

16. Example 2