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Both trapezoids and rectangles are quadrilaterals.
Squares, parallelograms, rhombuses, and trapezoids are quadrilaterals that are not rectangles.
squares, rectangles, rhombuses
A rectangle is not a rhombus.
The opposite sides of rectangles are the same length and parallel, and the angles are all right. All four sides of a rhombus must all be the same length and parallel, but the angles need not be right. Squares are both rectangles and rhombuses, but no other figure is both a rectangle and a rhombus. In other words, the union of the set of rhombuses with the set of rectangles is the set of squares.