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Some Special Parallelograms - Concept of Rhombus

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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°

Shaalaa.com | Property: The diagonals of a rhombus are perpendicular bisectors of one another

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