Q. 254.4( 14 Votes )
To Prove: Diagonals of a rhombus bisect each other at right angles.
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.
In ΔAOD and ΔAOB
AD = AB [Sides of a rhombus are equal]
OB = OD
Therefore, ΔAOD and ΔAOB are congruent.
∠ 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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