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In fact, some are rectangles, but not all are.
Yes, all rectangles are parallelograms. However, not all parallelograms are rectangles.
True
All parallelograms are not rectangles. The angles of a parallelogram need not be right angles and so the figure need not be a rectangle.
No. Rhombuses that are also rectangles are called squares. Rhombuses are parallelograms with 4 equal sides, while rectangles are parallelograms where all the angles are right.