Yes, it can... but does not have to. A parallelogram is a four-sided plane figure with opposite sides parallel. So as long as it has opposite sides that are parallel, it is a parallelogram.
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No, because to have a rectangle, you need to have four right angles, and parallelograms dont have to have right angles. However, all rectangles are parallelograms.
Parallelograms do not have right angles. A rectangle is a parallelogram but a parallelogram is not a rectangle.
Generally, there are no right angles in a parallelogram, but rectangles and squares can be seen as special parallelograms, as they have all the qualities needed to be classed as parallelograms, and in addition, they have four right angles.
When the corner angles are right-angles (90 degrees)
Rectangles are parallelograms with right angles.