| A polygon is a two-dimensional 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. |
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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 non-convex or concave. |
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Name each polygon by the number of sides and determine if it is convex or concave.
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This polygon has six sides so it is a hexagon. There are two interior angles measuring greater than 180º so it is concave.
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This polygon has fours sides so it is a quadrilateral. All of the interior angles measure less than 180º so it is convex.
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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.
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This polygon is equilateral but not equiangular so it is not regular.
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This polygon is equilateral and equiangular so it is regular.
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