The only characteristic a figure must have to be a quadrilateral is to be a four sided polygon.  Therefore every type of quadrilateral in this discussion can be produced from any quadrilateral.  This is because no matter what attribute you change to make a specific quadrilateral, whether it be the size of the angles or the length of a side, it is still a quadrilateral because it still has 4 sides.  In manipulating my original quadrilateral in GSP (figure 1), I was able to create all others including the ones shown above.
 

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