#### notes

Rhombus is also a parallelogram.

These are ,

1) The opposite angles of a rhombus are equal.

2) The opposite sides of a rhombus are parallel to each other.

3) The adjacent angles of a rhombus are supplementary.

4) The diagonals of a rhombus bisect each other.

There are exceptional properties of rhombus are

1) All the sides of a rhombus are equal.

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

**Property:** The diagonals of a rhombus are perpendicular bisectors of one another.

ABCD is a rhombus. Therefore it is a parallelogram too. Since diagonals bisect each other,

OA = OC and OB = OD.

We have to show that m∠AOD = m∠COD = 90°

It can be seen that by SSS congruency criterion

∆ AOD ≅ ∆ COD

Therefore, m ∠AOD = m ∠COD

Since ∠AOD and ∠COD are a linear pair,

m ∠AOD = m ∠COD = 90°