Question

prove that if the diagonal of a parallelogram bisect each other at right angle, it is a rhombus​

Answer 1

Take quadrilateral ABCD , AC and BD are diagonals which intersect at O.

In △AOB and △AOD

DO = OB ∣ O is the midpoint

AO=AO ∣ Common side

∠AOB = ∠AOD ∣ Right angle

So, △AOB ≅△AOD

So, AB = AD

Similarly, AB = BC = CD = AD can be proved which means that ABCD is a rhombus.