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What is a polygon defined as?

  1. A three-dimensional figure

  2. A simple, closed, two-dimensional figure

  3. A shape with curved lines

  4. A figure that does not have line segments

The correct answer is: A simple, closed, two-dimensional figure

A polygon is defined as a simple, closed, two-dimensional figure composed of straight line segments. These line segments, known as sides, meet at points called vertices. The defining characteristics of a polygon include having no curved edges and being closed, meaning that all points of the shape are connected without any gaps. In contrast, the other options describe different types of geometric figures. The first option refers to three-dimensional figures, which are not polygons because they extend into space rather than remaining in a two-dimensional plane. The third option describes shapes with curved lines, which are not polygons since such shapes include circles and ellipses, both of which have no straight edges. Finally, the fourth option refers to figures that do not consist of line segments at all, which again falls outside the definition of a polygon. Thus, the correct identification of a polygon as a simple, closed, two-dimensional figure is accurate.