Pythagorean theorem
Algebraic proofs

The theorem can be proved algebraically using four copies of the same triangle arranged symmetrically around a square with side c, as shown in the lower part of the diagram. This results in a larger square, with side a + b and area (a + b). The four triangles and the square side c must have the same area as the larger square,

giving

A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram. The triangles are similar with area 1 2 a b {\displaystyle {\tfrac {1}{2}}ab}, while the small square has side b − a and area (b − a). The area of the large square is therefore

But this is a square with side c and area c, so
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