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°