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Question

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Solution
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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, AOBAOD

So, AB=AD

Similarly, AB=BC=CD=AD can be proved which means that ABCD is a rhombus.

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