Prove a quadrilateral is a parallelogram

Minimum criteria needed to prove a quadrilateral is a parallelogram

A common type of proof involves proving that a quadrilateral is a parallelogram. If any of the 5 conditions below are met, then the quadrilateral must be a parallelogram.

• 1) If a quadrilateral has one pair of sides that are both parallel and congruent, then the quadrilateral is a parallelogram.
• 2) If a the opposite sides of a quadrilateral are congruent, then then quadrilateral is a parallelogram.
• 3) Opposites sides are parallel.
• 4) Opposite angles are congruent
• 5) Diagonals bisect each other.