No, all quadrilaterals are not parallelograms.
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All squares are quadrilaterals. All quadrilaterals are not squares. There is no square that is not a quadrilateral.
A square is a quadrilateral, but not all quadrilaterals are squares. A quadrilateral is just a four-sided figure.
All quadrilateral shapes have 4 sides
All trapezoids must be quadrilateral. And, as the name suggests a quadrilateral has four sides.
A quadrilateral is a polygon with 4 sides... so if it has 4 sides it is a quadrilateral. your question doesnt make sense because a 4 sided quadrilateral could be any quadrilateral at all.