quadrilateral
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a square , a rectangle, a trapezoid, a parallelogram, a rhombus
A rhombus cannot be a square. A rectangle is an equiangular parallelogram. A rhombus is an equilateral parallelogram. A square is an equilateral and equiangular parallelogram. Thus, a square is both a rectangle and a rhombus.
A rectangle is defined as: A quadrilateral with two sets of congruent sides. Therefore, a square is a TYPE of rectangle. Rectangles and squares belong to the set of parallelograms, so they have all properties of a parallelogram. A rectangle is an equiangular parallelogram, while a square is an equilateral and equiangular parallelogram. Thus, a square is a rectangle.
All four of the angles of a rectangle (and of squares) are right angles.(Its name comes from this : rect-angle.)
First of all, a trapezoid is not always a parallelogram. Did you mean the reverse: "Why is a parallelogram also a trapezoid"? If so, this depends upon your definition of a trapezoid and parallelogram. Some people define a trapezoid as a quadrilateral with exactly one pair of parallel sides, and a parallelogram as a quadrilateral with exactly two pairs of parallel sides. According to these definitions, a trapezoid can *NEVER* be a parallelogram, so your question is meaningless. However, others might define a trapezoid as a quadrilateral with one *or two* pairs of parallel sides. If you use this definition, then all parallelograms are also trapezoids, much in the same manner that all squares are also rectangles.