Question

Prove that the diagonals of a rhombus bisect
each other at right angle,​

Answer 1

Given: ABCD is a rhombus in which AB = BC = CD = AD. RTP: OD = OB and OA = OC Proof : From ΔAOB and ΔAOD AB = AD (From given) AO = AO (Common side) Since diagonals in rhombus perpendicular to each other ∠AOB =∠AOD = 90° ∴ ΔAOB ≅ ΔAOD (By RHS congruence) So. OD = OB ---- (1) (By CPCT) Similarly From ΔAOB and ΔBOC We can prove OA = OC ----- (2) Therefore, ,from (1) and (2) we can say that diagonals of a rhombus bisect each other.