# Proving a Quadrilateral is a Parallelogram

Students review the definition of a parallelogram and learn its converse, which states that if both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. Students also learn the following theorems related to parallelograms. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Students are then asked to determine whether given quadrilaterals are parallelograms based on these concepts, as well as solve problems related to these concepts using Algebra.