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

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Genius Quiz | Understanding Quadrilaterals20 mins
Quiz | Polygon & their Properties46 mins
Champ Quiz | Polygons (Quadrilaterals)30 mins
NCERT | Discussion on Imp. Qs. of Quadrilaterals43 mins
NCERT | Standard Form of Numbers41 mins
Champ Quiz | Spelling of important words47 mins
Benefits of Physical Activity36 mins
Champ Quiz | Revolt of 185749 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses