In elementary geometry, the parallelogram law states that the sum of the squares of the lengths of the fours sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. In case the parallelogram is a rectangle, the two diagonals are of equal lengths and the statement reduces to the Pythagorean theorem. But in general, the square of the length of neither diagonal is the sum of the squares of the lengths of two sides.
In inner product spaces, the statement of the parallelogram law reduces to the algebraic identity
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