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

To Prove: Diagonals of a rhombus bisect each other at right angles.

Concept Used:

All sides of a rhombus are equal.

SSS congruency: If all three sides of two triangles are equal, then they are called congruent.

Diagonals of a parallelogram bisect each other.

Diagram:

Proof:

In ΔAOD and ΔAOB

AD = AB [Sides of a rhombus are equal]

AO [Common]

OB = OD

Therefore, ΔAOD and ΔAOB are congruent.

So,

∠ AOD = ∠BOA [By C.P.C.T]

∠ AOD + ∠COD = 180˚ [Linear pair]

2 ∠ AOD = 180˚

∠ AOD = 90˚

And ∠ COD = 90˚

Hence, Diagonals of a rhombus bisect each other at right angles.