Question

prove that the diagonals of a rhombus bisect each other at right angles

Answer 1

Given that ABCD is a rhombus then AB = BC = CD = AD.

To prove that diagonals AC and BD bisect each other.

Proof : Given AB = CD.

In ΔAOB and ΔAOD

AO = AO (Common )

AB = AD (Given )

∠AOB + ∠AOD = 180° ( linear pair )

But ∠AOB = ∠AOD ( Vertically opposite angles)

∠AOB + ∠AOB = 180°

2∠AOB = 180° / 2

∠AOB = 90°

∴The diagonals AC and BD bisect each other