Q. 254.4( 14 Votes )

Prove that

Answer :

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.


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