A convex quadrilateral is a parallelogram if and only if any one of the following statements are true: 1. Each diagonal divides the quadrilateral into two congruent triangles with the same orientation. 2. The opposite sides are congruent in pairs. 3. The diagonals bisect each other. 4. The opposite angles are congruent in pairs. 5. The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law) 6.It possesses rotational symmetry. 7.One pair of opposite sides are parallel and congruent. 8.Two pairs of adjacent angles are supplementary.