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Pythagorean Theorem Project PDF Form

Pythagorean Theorem Project PDF Form

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suppose we have a right triangle with legs of length A and B and a hypotenuse of C we can draw an A by a square off the side of length a we can draw a b by b square off the side of length B and we can draw a c by C Square Off the hypotenuse though we leave the C by C Square unshaded the total shaded area in this diagram is a^2 + b^2 let's perform a few area preserving Transformations first we Shear each of the two squares along the opposite side of the triangle we rotate these sheared regions and then we Shear them down again filling the C by C Square since shearing and rotating doesn't affect the area we see that a^2 + b^2 must equal to c^2 so here we have a visual proof of the Pythagorean theorem which says that the sum of the squares of the legs of a right triangle must equal the square of the hypotenuse

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