Question

If the diagonals of a quadrilateral bisect one another at right angles, then the quadrilateral is a

• A. Trapezium
• B. Rectangle
• C. Rhombus
• D. None of these

Answer 1

Answer: (C)

Rhombus

Let $ABCD$ be a quadrilateral such that diagonals $AC$ and $BD$ bisect each other at right angle.

In $△AOB$ and $△AOD$

$DO=OB$ ........ ($O$ is the midpoint)

$AO=AO$ ........ (common side)

$\angle AOB=\angle AOD$ ...... (Right angle)

$⟹△AOB\cong △AOD$

$⟹AB=AD$

Similarly, we can prove $AB=BC=CD=AD$

Thus, $ABCD$ is a rhombus.

Hence, option C is correct.