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

Answers (1)
M mansi

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

To prove: ABCD is a rhombus.

Proof : In \triangleAOB and \triangleAOD,   

           

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

                BO=OD              (Given )

               AO=AO               (common)

             \triangleAOB \cong \triangleAOD   (By SAS)

                   AB=AD           (CPCT)

Similarly, AB=BC and BC=CD

Hence, it is a rhombus.

 

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