show that if the diagonal of a quadrilateral besect each other at right angle, then it is rhombus
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Take quadrilateral ABCD , AC and BD are diagonals which intersect at O.
In △AOB and △AOD
DO=OB ∣ O is the midpoint
AO=AO ∣ Common side
∠AOB=∠AOD ∣ Right angle
So, △AOB≅△AOD
So, AB=AD
Similarly, AB=BC=CD=AD can be proved which means that ABCD is a rhombus.
HENCE PROVED
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