Question

Prove that diagonals bisect each other in rhombus

Answer 1

Consider the rhombus ABCD

AB = BC = CD = DA (adjacent sides are equal)

In triangle AOD and triangle COD

OA = OC (diagonals of parallelogram bisect each other)

OD = OD (common)

AD = CD (proved above)

By SSS

triangle AOD is congruent to triangle COD

By CPCTC

Angle AOD = angle COD

angle AOD + angle COD = 180° (linear pair)

2 Angle AOD = 180°

angle AOD = 90°

Hence proved.