Question

ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2 = AC2 + BD2 .​

Answer 1

Let the diagonals AC and BD of rhombus ABCD intersect at O. Since the diagonals of a rhombus bisect each other at right angles. ∴ ∠AOB = ∠BOC = ∠COD = ∠DOA = 90º and AO = CO, BO = OD.
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