Prove that the diagonal of a Rhombus bisect each other at right angles.

ABCD is rhombus

AB = AD

also diagonals bisect each other

DO = OB

AO is common

so

Triangle AOD congruent to triangle AOB

so angle AOD = angle AOB…c.p.c.t.

but angle AOD + angle AOB = 180…linear pair

so angle AOD = angle AOB = 90