Characteristics of Polygons

Characteristics of a Polygon

• A polygon is a two-dimensional object consisting of a sequence of at least three segments of a line, with each segment sharing a common endpoint with the next.
• The endpoints of the segments are called vertices, and the segments themselves are called sides or edges.
• Each pair of consecutive sides of a polygon determines two angles: an interior angle and an exterior angle.

Classifications of Polygons

• A polygon can be classified as regular, irregular, concave, convex, simple, or complex.
• Regular polygons have congruent sides and interior angles.
• Irregular polygons have at least one pair of sides or interior angles that are not congruent.
• Concave polygons have a segment with endpoints inside the polygon and points on the segment that are outside the polygon.
• Convex polygons have any two interior points that determine a segment of line totally contained in the polygon.
• Simple polygons have segments that intersect only at vertices, while complex polygons have segments that intersect at points that are not vertices.

Examples of Polygons

• Figure 1 shows examples of regular, irregular, concave, convex, simple, and complex polygons.
• Figure 2 shows an isosceles triangle that is irregular.
• Figure 3 shows a convex quadrilateral and a concave hexagon.
• Figure 4 shows a simple polygon and a complex polygon.

Shapes that are Not Polygons

• A circle is not a polygon because it is not made up of straight line segments.
• Shapes with sides that are not straight, shapes that are not closed, and three-dimensional shapes are not polygons.
• Figure 5 shows examples of shapes that are not polygons, including a circle, a shape with a curved side, a shape that is not closed, and a three-dimensional shape.