Which property must be shown to prove that a quadrilateral is a parallelogram?

To demonstrate that a quadrilateral is a parallelogram, it is essential to establish that both pairs of opposite sides are congruent. This is a fundamental property of parallelograms, as it directly leads to the conclusion that opposite sides will not only be equal in length but also helps ensure that the shape fulfills the criteria of being a parallelogram.

When both pairs of opposite sides are shown to be congruent, it confirms that the quadrilateral has the necessary parallel properties, meaning that the opposite sides will extend infinitely and will never meet, maintaining equal distances apart. This congruence relationship is sufficient to prove that the opposite sides are parallel due to a property of Euclidean geometry known as the converse of the definition of parallelograms.

Other conditions could also establish that a quadrilateral is a parallelogram, such as having one pair of opposite sides that are both congruent and parallel or showing that the diagonals bisect each other. However, the choice indicating that both pairs of opposite sides are congruent is a definitive and commonly used method to prove the property of a parallelogram.