Final answer:
A quadrilateral with one pair of congruent opposite sides is not automatically a parallelogram. It needs additional properties such as both pairs of opposite sides being congruent or parallel, or having bisected diagonals, to be considered a parallelogram.
Step-by-step explanation:
If one pair of opposite sides of a quadrilateral is congruent, the quadrilateral is not necessarily a parallelogram. However, for a quadrilateral to be a parallelogram, along with having one pair of opposite sides that are congruent, there are additional properties that must be met. These include having both pairs of opposite sides congruent, having both pairs of opposite sides parallel, or having one pair of opposite sides both congruent and parallel. Furthermore, if the diagonals bisect each other, or if one pair of opposite angles are congruent, these conditions also suggest that the quadrilateral can be classified as a parallelogram. To ensure the quadrilateral is a parallelogram when one pair of opposite sides is congruent, there should be additional verifiable properties such as congruent angles, parallel sides, or bisected diagonals. For example, if the congruent sides are also parallel, this would fulfill the parallelogram properties and confirm the quadrilateral's classification as a parallelogram.