A rectangle is a polygon because it is a closed two-dimensional shape formed by four straight sides. The sides meet at right angles, and it has four vertices, which satisfies the definition of a polygon.
A circle, on the other hand, is not a polygon. This is because it does not have straight sides or vertices; instead, it is a curved shape where every point on the circumference is equidistant from the center. Since polygons must be made up of straight line segments, a circle fails to meet this criterion.
Similarly, an ellipse is also not a polygon. Like the circle, an ellipse consists of a curved boundary without any straight edges or vertices. It is defined by the set of points where the sum of the distances to two focal points is constant, which again does not correspond with the definition of a polygon.
In summary, while a rectangle is a polygon, both a circle and an ellipse are not because they lack straight edges and vertices, which are essential characteristics of polygons.