A polygon is a closed figure made up of straight line segments. The word polygon comes from Greek: poly meaning many, and gon meaning angles. Key characteristics of polygons include being a closed figure with straight sides, having vertices or corners, and containing interior angles. Examples include triangles and squares, while circles and open shapes are not polygons.
Polygons have three key properties. First, vertices are the corner points where sides meet. Second, sides are the line segments connecting these vertices. Third, interior angles are formed inside the polygon at each vertex. There's an important relationship: the number of vertices always equals the number of sides in any polygon.
Polygons are classified by their number of sides. A triangle has 3 sides, a quadrilateral has 4, a pentagon has 5, hexagon has 6, heptagon has 7, and octagon has 8 sides. This pattern continues with nonagon having 9 sides and decagon having 10. As the number of sides increases, the polygon becomes more complex and approaches the shape of a circle.
Polygons can be classified as regular or irregular. Regular polygons have all sides equal in length and all angles equal in measure, creating symmetrical shapes. Irregular polygons have sides of different lengths or angles of different measures, making them asymmetrical. We can identify regularity by measuring the sides and angles - if they're all equal, the polygon is regular.
Polygons can also be classified as convex or concave. Convex polygons have all interior angles less than 180 degrees and no indentations. Any line segment between two points inside a convex polygon stays completely inside. Concave polygons have at least one interior angle greater than 180 degrees, creating dents or indentations. In concave polygons, some line segments between interior points will pass outside the polygon.