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Pythagorean Theorem

Explore the Pythagorean Theorem with this detailed, step-by-step guide using right triangles. Start by labeling the sides of the triangle as a, b, and c. Construct squares on each side, find the center by drawing diagonals, and create a parallelogram that demonstrates the theorem visually. This method shows that the sum of the squares of the legs (a² + b²) equals the square of the hypotenuse (c²). Perfect for visual learners, this explanation breaks down the theorem into easy-to-follow steps.

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Pythagorean Theorem

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Presentation Transcript

  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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