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Geometric proofs using vectors

Prove the sum of the squares of the lengths of a parallelogram’s diagonals is equal to the sum of the squares of the lengths of the sides.

u2-t3-s2-d3

Interactive

Sum of diagonal squares equals sum of side squares

demo

In a parallelogram, |d₁|² + |d₂|² equals the sum of the side squares. Drag and step the vector expansion.

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