Any other shape with more than 4 sides
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No. They cannot be similar because a parallelogram has two pairs of sides with equal length. A parallelogram cannot have more than one pair.
Yes all rectangles are parallelogram but all parallelogram cannot be rectangles.
A parallelogram can have adjacent sides and angles which are different. A square cannot.
No, a trapezoid cannot be be a parallelogram.
No, a parallelogram cannot be a trapezium.