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Question

If the diagonals of a quadrilateral ABCD bisect each other at the point O then the quadrilateral ABCD can be a _____.

A
Trapezium
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B
Kite
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C
Parallelogram
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D
None of the above
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Solution

The correct option is C Parallelogram
From the given figure, consider the triangles AOB and COD.
AO = OC (Given)
BO = OD (Given)
AOB=COD ( vertically opposite angles)AOBCOD

By corresponding parts of congruent triangles,
ABO=CDO-------(i)

But, (i) forms alternate interior angles. Hence, AB || CD.
Similarly, AD || BC.
Since, both the pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

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