Question

1. which statement requires additional information to prove that a quadrilateral is a parallelogram? one pair of opposite sides of the quadrilateral is both parallel and congruent. one pair of opposite sides of the quadrilateral is parallel. the diagonals of the quadrilateral bisect each other. both pairs of opposite angles of the quadrilateral are congruent.

Explanation:

Step1: Recall parallelogram properties

A parallelogram has both pairs of opposite sides parallel, both pairs of opposite sides congruent, both pairs of opposite angles congruent and diagonals that bisect each other.

Step2: Analyze each option

• If both pairs of opposite angles of a quadrilateral are congruent, it is a parallelogram.
• If the diagonals of a quadrilateral bisect each other, it is a parallelogram.
• If one pair of opposite sides of a quadrilateral is both parallel and congruent, it is a parallelogram.
• If only one pair of opposite sides of a quadrilateral is parallel, it could be a trapezoid. We need more information (like the lengths of the sides or the other - pair of sides being parallel) to prove it is a parallelogram.

Answer:

One pair of opposite sides of the quadrilateral is parallel.