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A quadrilateral is a parallelogram with four sides. For example: square, rectangle, parallelogram, trapezoid, rhombus, diamond...
A parallelogram must have 4 sides and so it must be a quadrilateral. However, the sides of a quadrilateral need not be parallel so a quadrilateral need not be a parallelogram.
A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.
In this case, the quadrilateral is sometimes a parallelogram.
No. A quadrilateral is a parallelogram when consecutiveangles are supplementary.