Trapezoids are one of the most common quadrilaterals. A trapezoid has one pair of parallel sides. When a trapezoid has two sets of parallel sides, it is a more specific type of trapezoid called a parallelogram. A more specific type of trapezoid is called an isosceles trapezoid. In addition to one pair of parallel sides, isosceles trapezoid properties include congruent legs, base angles and diagonals.