Not necessarily. A quadrilateral is a plane shape with four straight sides. There is no requirement for a side to be parallel to another.
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No, and all parrallelograms are not quadralaterals.
No but they are all 4 sided quadrilaterals
A circle and an ellipse. Neither of them are polygons and so cannot be quadrilaterals, still less parallelograms.
Yes, except that the word is parallelogram.
Opposite angles are congruent in a parallelogram.