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No trapezoids are parallelograms, and no parallelograms are trapezoids.
By definition, all squares are parallelograms. Not all parallelograms, however, are squares. All rectangles and rhombuses are also parallelograms.
No trapezoids are parallelograms, and no parallelograms are trapezoids.
Yes all squares are parallelograms but not all parallelograms are squares.
It is sometimes true that two parallelograms are similar. The could be congruent, or dissimilar in that one is not an enlargement of the other.