All 4 sided parallelograms are quadrilaterals.
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All parallelograms are quadrilaterals but all quadrilaterals are not necessarily parallelograms
Some parallelograms could be quadrilaterals but all parallelograms are polygons
parallelograms and,or quadrilaterals
Parallelograms are a special form of quadrilaterals (four sided polygons). Parallelograms have 2 sets of parallel sides. So you could say that all parallelograms are quadrilaterals. Or you could say that all parallelograms are polygons. I'm not sure what you are asking.
No, a quadrilateral isn't always a trapezoid. One way to consider it is that all trapezoids are quadrilaterals (four-sided shapes), but not all quadrilaterals are trapezoids. Some quadrilaterals are concave quadrilaterals, some are scalene convex quadrilaterals (called trapezoids in the UK), some would be trapezoids, and some would be parallelograms (rectangles, squares, rhomboids, rhombi). If parallelograms are considered a special case of trapezoids, then trapezoids would include all non-scalene convex quadrilaterals, which is a highly inclusive definition.