Draw a line touching one side to the opposite side of the square, which is not parallel to any side, and does not touch any vertex, so you will have two new quadrilaterals, each one has one pair of parallel sides and one pair of nonparallel sides.
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Draw one line vertically - splitting the square in half, and draw one line diagonally - corner to corner.
They can, if you start off with a square, and make a diagonal line from a little out on the top line to the bottom right-hand corner.
Yes, the trapezoid's angles must be 90 degrees however.
you can make a square based pyramid using 4 triangles and a 1 square
you can make 2 trapezoids