I remember teaching quadrilaterals and creating a tree diagram to differentiate and connect the characteristics of quadrilaterals. Stemming out of quadrilaterals, the parallelogram then breaks up into rhombii and rectangles, which then combine to form a square. The trapezoid drops down into its own stem and then from the trapezoid was the special isosceles trapezoid. Since parallelograms must have two pairs of parallel sides, the trapezoid only has two parallel sides and no more. Otherwise we would be able to categorize some trapezoids as parallelograms.