Question

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

Answer 1

The diagonals of a rhombus bisect each other at right angles.

Explanation:

Given: ABCD is a rhombus. So AB = BC = CD = AD.

To prove: Diagonals AC and BD bisect each other at right angles.

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 at right angles.