Trapezoids

                    General Trapezoid                                                  rectangle                                         Square
 

Isosceles Trapezoid                    Parallelogram

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Trapezoids are made up of at least one set of opposite parallel lines (some will argue for EXACTLY one set of opposite parallel lines but not me!)  and 4 sides.  This leaves a lot of room for manipulation.  Let's look:
 

Parallelogram?   Yes, any.  To produce any parallelogram from a general trapezoid, a manipulation of the lengths of the sides and the some angles.  The parallel sides will remain parallel.... therefore, the parallelogram produced is still a trapezoid.

Rectangles?  Squares?  Rhombus?   Yes, any.  When a trapezoid is manipulated to have 2 sets of parallel sides with 90 degree interior angles, it is then a rectangle. Then, if it is manipulated so that all sides are equal (keeping 90 degree angles and parallel sides),  it becomes a square.  From that, the angles can be changed around (keeping the lengths and the parallel sides) and you would get a rhombus.  Throughout all 3 manipulations, the figure still maintains the minimum characteristics of a trapezoid.

Isosceles Trapezoid?   Yes, all.  Any general trapezoid can be manipulated into any isosceles trapezoid simply by making one set of opposite sides equal lengths (particularly the non parallel sides if such exist.)  Thus, the isosceles trapezoid is a special case of a trapezoid, as it's name suggests.
 

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