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Question

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

A
square
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B
parallelogram
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C
rhombus
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D
trapezium
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Solution

The correct option is A square
ΔAOB,ΔAOD
DO=OD ( mid point )
AO=OA (common side)
AOB=AOD (right angle )
So ΔAOB,ΔAOD
So AB=AD
And ABc=ADC=900
Similarly AB=BC=CD=AD can be proved that ABCD is a square

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