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A quadrilateral MUST be a parallelogram if it has both pairs of its opposite sides parallel.
A quadrilateral MUST be a parallelogram if it has both pairs of its opposite sides congruent (or equal in measure).
A quadrilateral MUST be a parallelogram if it has one pair of opposite sides both parallel and congruent.
A quadrilateral MUST be a parallelogram if it has both pairs of its opposite angles congruent (or equal in measure).
A quadrilateral MUST be a parallelogram if it has both diagonals bisecting each other.
A quadrilateral MUST be a parallelogram if it has all of its pairs of consecutive angles supplementary.
Edwin