If diagonals of a parallelogram bisect each other at right angles, prove it is a rhombus. (NCERT Class 9/10)

Answer: In parallelogram ABCD, diagonals bisect each other at O and are perpendicular. In right triangles AOB and AOD: AO common, BO=DO, right angles at O ⇒ congruent (RHS), giving AB=AD. Similarly all sides equal ⇒ rhombus.