so that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus
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Step by step explination-
Take a quadrilateral ABCD, AC and BD are diagonals which intersect at O.
In triangle AOB and Triangle AOD
DO=OB ( Mid point)
angle AOB = angle AOD (right angle)
therefore triangle AOB is congruent to triangle AOD
So, AB =AD
In the same way we can prove that
AB = BC = CD = AD
Therefore ABCD is a rhombus
Hence proved
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