You can drag any of the named vertices to change the quadrilateral.
The the rectangle makes only rectangles (everything you can drag it to--except a single line--is a rectangle)
The same is true of the square, the rhombus and the parallelogram.
The kite only makes kites except if you make two of the sides in a straight line with each other, and then it's a triangle. A triangle is not a kind of a kite.
The trapezoid makes only trapezoids except if you make OQ and PR parallel to each other. The usual US definition of trapezoid says that a parallelogram isn't a trapezoid. On the other hand, if you read a Canadian math book (or a few US math books), you'll find that's allowed as a special kind of trapezoid. The definition of trapezoid is not completely consistent.