Question

Diagonals of a rhombus bisect each other at ______ angles.

• A. $90°$
• B. $10°$
• C. $360°$
• D. $60°$

Answer 1

The correct option is A $90°$

Let $ABCD$ is a rhombus.
$\Rightarrow AB=BC=CD=DA$ [ Adjacent sides are equal in rhombus ]
In $\Delta AOD$ and $\Delta COD$
$\Rightarrow OA=OC$ [ Diagonals of rhombus bisect each other ]
$\Rightarrow OD=OD$ [ Common side ]
$\Rightarrow AD=CD$
$\therefore \Delta AOD\cong \Delta COD$ [ By SSS congruence rule ]
$\Rightarrow \angle AOD=\angle COD$ [ CPCT ]
$\Rightarrow \angle AOD+\angle COD=180°$ [ Linear pair ]
$\Rightarrow 2\angle AOD=180°$
$\therefore \angle AOD=90°$
Hence, the diagonals of a rhombus bisect each other at right angles.