Squares

                    square                        equilateral rhombus                   equilateral rectangle, trapezoid, etc...

When manipulating the square in GSP, the size and position of the square could be changed but nothing else.   The interior angles remained 90 degrees each and the sides remained all equal lengths.  Also, opposite sides remained parallel to eachother.

Therefore, all other quadrilaterals could be formed from a square but only in special cases.  The special cases must have the following 3 traits:
        1.  Equal sides
        2.  Interior angles that equal 90 degrees
        3.  Opposite sides are parallel

For example, a rectangle is a special case of a square if it satisifies the above three traits.  However, if one set of parallel sides were longer than the other set, the rectangle would no longer be a special case of a square.
 
 

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