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(D) According to the Varignon's Theorem,the figure formed by joining the mid-points of the sides of any quadrilateral is a parallelogram.For this para

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diagonals of $ABCD$ are equal and perpendicular

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(D) According to the Varignon's Theorem,the figure formed by joining the mid-points of the sides of any quadrilateral is a parallelogram.For this parallelogram to be a square,the sides must be equal and the adjacent sides must be perpendicular.The sides of the quadrilateral formed by joining the mid-points are parallel to the diagonals of the original quadrilateral $ABCD$ and are equal to half the length of the diagonals.Therefore,for the resulting figure to be a square,the diagonals of the original quadrilateral $ABCD$ must be equal in length (to make the sides of the parallelogram equal) and perpendicular to each other (to make the angles of the parallelogram $90^{\circ}$).

The figure formed by joining the mid-points of the sides of a quadrilateral $ABCD,$ taken in order,is a square only if,

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