Characteristics of a Polygon

Characteristics of a Polygon

• A polygon is a two-dimensional object consisting of a sequence of at least three segments of a line.
• The endpoints of the segments are called vertices, and the segments are called sides or edges.
• Each pair of consecutive sides of a polygon determines two angles: an interior and an exterior angle.
• An exterior angle is one that contains points outside the polygon, and the interior angle is the other angle by exclusion.

Types of Polygons

• Regular Polygons: Equilateral and equiangular, with congruent sides and interior angles.
• Irregular Polygons: Not regular, with at least one pair of sides or interior angles that are not congruent.
• Concave Polygons: A polygon that is not convex, with a segment where the endpoints are inside the polygon, but there are points on the segment that are exterior to the polygon.
• Convex Polygons: A polygon where any two interior points determine a segment of line totally contained in the polygon.
• Simple Polygons: Segments of a polygon intersect only on the vertices.
• Complex Polygons: Segments of a polygon intersect on points that are not vertices of the polygon.

Shapes that are Not Polygons

• Circles: Not polygons, as they do not consist of segments of a line.
• Shapes with non-straight sides: Not polygons, as they do not meet the definition of a polygon.
• Open shapes: Not polygons, as they are not closed.
• Three-dimensional shapes: Not polygons, as they are not two-dimensional.

Learn about the definition and properties of polygons, including their sides, vertices, and angles.