This document classifies and defines different types of quadrilaterals including parallelograms, rectangles, squares, rhombuses, trapezoids, and kites. It notes that parallelograms have opposite sides that are parallel and congruent and opposite angles that are congruent. Rhombuses and squares are specific types of parallelograms where all sides are congruent, and squares are also rectangles. Trapezoids have only one pair of parallel sides, while kites have adjacent congruent sides and opposite congruent angles.