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

Take quadrilateral ABCD , AC and BD are diagonals which intersect at O.In ΔAOB and ΔAOD
DO=OB O is the midpoint
AO=AO Common side
∠AOB=∠AOD Right angle
So, ΔAOB≅ΔAOD
So, AB=AD
Similarly, AB=BC=CD=AD can be proved which means that ABCD is a rhombus.