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Proving Quadrilaterals are Parallelograms Geometry Definition of Parallelogram If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. How to Prove Parallelograms If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. How to Prove Parallelograms If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram How to Prove Parallelograms If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. How to Prove Parallelograms If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. How to Prove Parallelograms If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. Proving Quadrilaterals are Parallelograms • Show that both pairs of opposite sides are parallel. • Show that both pairs of opposite sides are congruent. • Show that both pairs of opposite angles are congruent. • Show that one angle is supplementary to both consecutive angles. • Show that the diagonals bisect each other. • Show that one pair of opposite sides are congruent and parallel.
