A rectangle (opposite sides are parallel which is a parallelogram!)
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All rectangles are parallelograms but a rhombus for example, is a parallelogram but not a rectangle.
No as for example the diagonals of a rectangle are equal in length whereas they are not equal in length in a parallelogram
Yes, a parallelogram has 2 pairs of symmetrical sides. A rectangle is an example of a parallelogram but with all of its angles being 90 degrees whereas in a typical parallelogram none of the angles are 90 degrees. Opposite sides will be of equal lengths.
A parallelogram is just one example of a four-sided polygon. The general terms for four-sided polygons are quadrilateral, quadrangle, and tetragon.
No, a parallelogram is not a trapezoid.