Q. 54.8( 8 Votes )

Prove that the diagonals of a rhombus bisect each other at right angles.

Answer :


Let ABCD be a rhombus whose diagonal AC and BD intersect at the point O.


As we know that the diagonals of a parallelogram bisect each other and rhombus is a parallelogram.


So, OA=OC and OB=OD.


From ∆ COB and ∆ COD we get,


CB = CD (sides of rhombus) and


CO is common in both the triangles.


So, OB = OD


Therefore, by SSS theorem.


∆ COB ∆ COD


COB = COD


COB + COD = 180° (Linear pair of angles)


Thus, COB = COD = 90°


Hence, the diagonals of a rhombus bisect each other at right angles.


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