Question

In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD is a

• A. square
• B. parallelogram
• C. rhombus
• D. trapezium

Answer 1

The correct option is A square

$\Delta AOB,\Delta AOD$

DO=OD ( mid point )

AO=OA (common side)

$\angle AOB=\angle AOD$ (right angle )

So $\Delta AOB,\Delta AOD$

So AB=AD

And $\angle ABc=\angle ADC={90}^0$

Similarly AB=BC=CD=AD can be proved that ABCD is a square