A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram, plus the following: 1  The diagonals are congruent. parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A parallelogram also has the following properties: 1  Opposite angles are congruent; 2  Opposite sides are congruent; 3  Adjacent angles are supplementary;