Question: prove that in a parallelogram each pair of opposite sides are congruent?
Answer: THEOREM: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram. ... THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. * THEOREM: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.