A right angle.
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All rectangles are parallelograms, so yes there are some.
Some parallelograms are rectangles; all rectangles are parallelograms.
Some do, but not all. It's not a general thing that you can say about all parallelograms.
No. Only some parallelograms are rectangles. But all rectangles are parallelograms.
No trapezoids are not parallelograms. Trapezoids are actually quadrilaterals and they have one pair of opposite sides. Parallelograms by definition have 2 pairs of parallel sides.