Lesson PROOF of Pythagorean Theorem

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 See also: the Wikipedia article on the Pythagorean_theorem. Pythagorean theorem was proven by an ancient Greek named Pythagoras, and says that for a right triangle with legs A and B, and hypotenuse C , , .
 To the left is an animated proof of the Pythagorean Theorem. Starting with a right triangle and squares on each side, the middle size square is cut into congruent quadrilaterals (the cuts through the center and parallel to the sides of the biggest square). Then the quadrilaterals are hinged and rotated and shifted to the big square. Finally the smallest square is translated to cover the remaining middle part of the biggest square. A perfect fit! Thus the sum of the squares on the smaller two sides equals the square on the biggest side. What this means in plain language: As you know, the area of a square is the length of its side, multiplied by itsemf (squared). For instance, the area of a square room that is 10 by 10 feet is 10 multiplied by 10, that is, 100 square feet. What this animated proof says is this: take a square whose side is the same as the hypothenuse (green square). You can take scissors and cut this square into pieces that can be REASSEMBLED to become two squares. These two squares would be with the sides of the same length as the sides of the right triangle. Because cutting the big square with scissors and reassembling it into smaller pieces did not change the total \ area of the piece of paper, we now know that the area of the big square is the sum of areas of the small squares,\ or
For in depth treatment of this wonderful theorem and various proofs, go to MathWorld, or see these lessons The Pythagorean Theorem and More proofs of the Pythagorean Theorem in the current module.

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