We have to find the ways to prove that a quadrilateral is a parallelogram.
There are six ways to prove that a quadrilateral is a parallellogram:
1) Prove that opposite sides are congruent. Congruent sides are identical, and the parallelogram have 2 pair of congruent sides. You can prove it by using a diagonal to divide the parallellogram in two triangles and prove that this triangles are congruent. Then, the opposites sides are congruent too.
2) Prove that opposite angles are congruent. As the opposite sides are parallel, the angles that are opposite of each other have the same measure.
3) Prove that opposite sides are parallel.
4) Prove that consecutive angles are supplementary. This is a property of parallellograms, as the angles are consecutive and the sides are parallel.
5) Prove that an angle is supplementary to both its consecutive angles. This is the previous property extended to both sides from an angle.
6) Prove that quadrilateral's diagonals bisect each other. This can only happen when opposite sides are congruent, which is a property of parallellograms.