In manipulating the rectangle drawn in GSP, the above variations were created.  The lengths of the sides could be changed; however, the lengths of opposite sides remained the same.  Also, the interior angles always remained 90 degrees.  Also, the position of the rectangle could be changed by rotating the entire shape.

Square?  Yes, always.  The interior angles of a rectangle are always 90 degrees and the opposite sides are parallel so the only change needed would be to make each side the same length.  In doing that, the figure is still a rectangle and also a square.

Rhombus?  Yes, some.  In the case that the rectangle has sides that are all the same length, all  conditions of rhombus are satisfied.  To produce a rhombus from any rectangle, just make all sides equal in length.  Note that this special case of a rhombus is also a square.  The rectangle is unable to produce a rhombus with interior angles different from 90 degrees.

Parallelogram?  Yes, some.  A rectangle can only produce parallelograms with opposite sides of equal lengths and with interior angles of 90 degrees.

Trapezoid?  Yes, some.  A rectangle is always the special case of a trapezoid in which both sets of opposite sides are parallel.  However, a retangle is unable to produce a trapezoid with only one set of parallel lines.

Isosceles Trapezoid?  Yes, some.  A rectangle is always the special case of an isosceles trapezoid which 2 sets of parallel sides because a rectangle always has opposite sides of the same lengths. A rectangle cannot produce any trapezoids with only one set of parallel sides.

Quadrilateral?  Yes, some.  A rectangle can produce any quadrilateral with the following traits: 1. two sets of opposite sides that are parallel and equal in length
2.  all interior angles are equal to 90 degrees.
 

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