1. Pythagorean Theorem step by step a c b Picture This!

2. start with a right triangle

3. a label the sides c b

4. a construct a square on each side c b

5. find the center of the square on a by drawing its diagonals a c b

6. Then copy side c a c b

7. and slide it over−parallel to side c a c b to the center of the square on a

8. Draw the perpendicular bisector a c b

9. The 2 perpendicular bisectors at the center divide the square into a c b 4 equal parts

10. The length of each arm radiating out from the center is equal to half of side c c c 2 c 2 c 2 c 2

11. Sliding side c along the base to the center of the square c also makes a parallelogram

12. So side b of the triangle is equal to the long side of the quadrilateral. c b b plus the shortest side of the quadrilateral

13. slide the 4 quadrilaterals over to the big square a c b

14. The outsides fit because each one is half of side c. a c b

15. The insides fit because each one equals side b plus the short side a c b

16. The square on b fills the space in the middle of the square on c so we’re done! a c b

17. a c b for right triangles... We had to cut up the square on side a to do it, but we proved that

18. a c b the sum of the squares on the legs

19. a c b is equal to the square on the hypotenuse

20. a c b a2a2 +b2b2 = c2c2