6.1.1 Properties and Attributes of Polygons Key Objectives • Classify polygons based on their sides and angles. • Find and use the measures of interior and exterior angles of polygons. Key Terms • Each segment that forms a polygon is a side of a polygon . • The common endpoint of two sides is a vertex of the polygon .
• A segment that connects any two nonconsecutive vertices is a diagonal . • A regular polygon is one that is both equilateral and equiangular. • A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. • If no diagonal contains points in the exterior, then the polygon is convex . Theorems, Postulates, Corollaries, and Properties • Polygon Angle Sum Theorem The sum of the interior angle measures of a convex polygon with n sides is ( n − 2)180°. • Polygon Exterior Angle Sum Theorem The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360°. Example 1 Identifying Polygons A polygon is a closed figure on a plane formed by three or more line segments that intersect only at their endpoints.
Three figures are determined to be polygons or not polygons. The polygons are named according to the number of sides they have. The first and third figures are closed figures with only one interior and one exterior. The line segments defining each figure intersect only at their endpoints. These two figures are polygons. The second figure contains line segments that intersect away from their endpoints. It is not a polygon. The first figure has four sides; it is called a quadrilateral. The third figure has nine sides; it is called a nonagon.
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