Quadrilateral to be a Parallelogram

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We can state the defining property of a parallelogram as follows:

"If a quadrilateral is a parallelogram, then its opposite sides are equal".

Converse

"If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram".

The converse statement stated above is a necessary condition for a quadrilateral to be a parallelogram. Similarly, we may formulate the following two other conditions for a quadrilateral to be a parallelogram.

• "If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram".

• "If either pair of opposite sides of a quadrilateral are equal and parallel, the quadrilateral is a parallelogram".