No because squares have different properties compared to parallelograms but they are both 4 sided quadrilaterals.
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Not all of them have 4 right angles for example a rhombus does not have any right angles, yet it is still a parellegram so parellegrams don't always need to have 4 right angles.
No, rectangles are not squares
No but all squares are a rectangles
no, but all squares are rectangles
All squares are rhombi