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The picture you are looking for is a parallelogram.
A B . . D C . . Parallelogram ABCD.
A rectangle has 4 equal, 90 degree angles (one at each corner). A parallelogram may not have all equal angles. Imagine a rectangle that whose opposite corners were pulled so that it had two slanted, but parallel sides, and two straight and parallel sides. That is what some parallelograms look like. A rectangle, however, is a type of parallelogram. You can see a picture of a non-rectangular parallelogram, by clicking on the related link.
No, a parallelogram is not a trapezoid.
Square = parallelogram and a square trapezoid = trapezoid Parallelogram = Parallelogram