Question: prove that if the opposite sides of a quadrilateral are equal the figure is a parallelogram?
Answer: Theorem 47: If both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. ... Theorem 49: If one pair of opposite sides of a quadrilateral is both equal and parallel, then it is a parallelogram. Theorem 50: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.