By pairing the vertices of a given quadrangle we draw lines joining them and the lines intersect forming triangles with the sides of the quadrangle. We now project the points of intersection, located outside the quadrangle, to infinity.
When we do this, does the quadrangle transform to a rectangle or a parallelogram?
I remember to have read that the quadrangle transforms to a parallelogram. There are four possible parallelograms, but only one possible rectangle. In addition, unbiased symmetry accrues through a rectangle. Whereas, each of the four parallelograms is associated with a certain bias. Therefore, when a particular parallelogram is chosen, an explanation is called for, for choosing that bias.
Not knowing how to choose among the parallelograms, I seek guidance.