A polygon is a twodimensional closed figure of three or more line segments (sides) connected end to end. Each segment is a side and only intersects the endpoints of the two adjacent sides. Each point of intersection is a vertex. At right are two examples of polygons. 


Which of the following are polygons? If not, explain why not.
Shapes A, C, and F are polygons. Shape B is not connected. Some of the sides in shape D
intersect more than two other sides. Shape E is not completely made by line segments.
NAMING POLYGONS
Polygons are named by the number of sides they have.
A polygon is convex if each of the interior angles measures less than 180º. If a polygon has any interior angle measuring greater than 180º (a reflex angle), then the polygon is nonconvex or concave. 


Name each polygon by the number of sides and determine if it is convex or concave.
This polygon has six sides so it is a hexagon. There are two interior angles measuring greater than 180º so it is concave.


This polygon has fours sides so it is a quadrilateral. All of the interior angles measure less than 180º so it is convex.

If all of the sides of a polygon are congruent, it is called equilateral. If all of the angles are congruent, it is called equiangular. If a polygon is both equilateral and equiangular, then it is a regular polygon.
Determine if each polygon is regular.
This polygon is equilateral but not equiangular so it is not regular.


This polygon is equilateral and equiangular so it is regular.
