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Pythagorean Theorem

Picture This!. Pythagorean Theorem. c. a. step by step. b. start with a right triangle. label the sides. c. a. b. construct a square on each side. c. a. b. find the center of the square on a by drawing its diagonals. c. a. b. Then copy side c . c. a. b.

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Pythagorean Theorem

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

  2. start with a right triangle

  3. label the sides c a b

  4. construct a square on each side c a b

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

  6. Then copy side c c a b

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

  8. Draw the perpendicular bisector c a b

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

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

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

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

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

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

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

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

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

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

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

  20. a2 + b2 = c2 c a b

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