Yes they are special rectangles that are tilted over
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Parallelograms are a special form of quadrilaterals (four sided polygons). Parallelograms have 2 sets of parallel sides. So you could say that all parallelograms are quadrilaterals. Or you could say that all parallelograms are polygons. I'm not sure what you are asking.
The simple answer is no, not all parallelograms have at least one right angle. However, there are some that do. Rectangles and squares are 'special' parallelograms that all have at least one right angle.
the three special quadrilaterals that can be a parallelogram are a rectangle, a square, and a rhombus Actually, this is incorrect. All squares are rectangles. All rectangles are parallelograms. Therefore all squares are parallelograms. But not all parallelograms are rectangles. And not all rectangles are squares.
No trapezoids are parallelograms, and no parallelograms are trapezoids.
No trapezoids are parallelograms, and no parallelograms are trapezoids.