This document discusses several theorems for proving that a quadrilateral is a parallelogram: 1) If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram. 2) If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram. 3) If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram. The document also provides proofs of these theorems and discusses using coordinate geometry to prove sides are congruent or parallel.