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Show that if the diagonals of a quadrila...

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

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Proof:
In 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`
`:.ABCD` is a rhombus.
Hence Proved.
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