Q

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

Q : 3  Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

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Given: the diagonals of a quadrilateral bisect each other at right angles i.e.BO=OD.

To prove: ABCD is a rhombus.

Proof : In $\triangle$AOB and $\triangle$AOD,

$\angle AOB=\angle AOD$        (Each $90 \degree$)

BO=OD              (Given )

AO=AO               (common)

$\triangle$AOB $\cong$ $\triangle$AOD   (By SAS)

Similarly, AB=BC and BC=CD

Hence, it is a rhombus.

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