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

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

To prove: ABCD is a rhombus.

Proof : In AOB and AOD,

(Each )

BO=OD              (Given )

AO=AO               (common)

AOB  AOD   (By SAS)

Similarly, AB=BC and BC=CD

Hence, it is a rhombus.

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