One proof regarding a parallelogram is used to show that the two pairs of opposite sides are congruent. When given a parallelogram with angles A, B, C and D, the line segments AB and CD are congruent, as are the line segments BC and AD.
Another proof relating to parallelograms states that a quadrilateral for which one pair of opposite sides is both parallel and congruent is a parallelogram. This proof is developed using geometric properties, including those belonging to transversals, interior angles, congruent sides of triangles and corresponding parts of congruent triangles. A parallelogram is a quadrilateral for which both pairs of opposite sides are parallel and congruent, with related properties applying to the shape's angles.