Yes.
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Square = parallelogram and a square trapezoid = trapezoid Parallelogram = Parallelogram
Yes, a square is a special type of parallelogram. Every square has two pairs of parallel sides, which is the condition for being a parallelogram.
Yes. A square is a special type of rhombus which is itself a special kind of parallelogram.
A square is a special case of a rhombus. A parallelogram is not a rhombus.
A square is a special case of a parallelogram.