How are polygons classified? 6-1B Exploring Polygons How are polygons classified?

You measured one-dimensional figures. Identify and name polygons.

Definitions A polygon is a closed figure formed by a finite number of coplanar segments called sides such that The sides that have a common endpoint are noncollinear, and Each side intersects exactly two other sides, but only at their endpoints.

Definition A vertex of a polygon is the vertex of each angle in the polygon. A polygon is named by the letters of its vertices, written in order of consecutive vertices.

Definition A convex polygon is one in which each diagonal (except its endpoints) is in the interior (inside) of the polygon.

Convex Polygons

Definition A concave polygon is one in which at least one diagonal (except its endpoints) is not in the interior of the polygon. Opps…

Concave Polygons

Not Polygons

Definition An Equilateral polygon is a polygon in which all sides are congruent.

Definition An Equiangular Polygon is a polygon in which all angles are congruent.

Definition A regular polygon is a polygon that is both equilateral and equiangular. An irregular polygon is a polygon that is not regular

Classification of Polygons sides Triangle sides Quadrilateral sides Pentagon sides Hexagon sides Heptagon sides Octagon sides Nonagon sides Decagon sides Dodecagon 20 sides Icosagon “n” sides n-gon See page 57 for chart

Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular

Name and Classify Polygons B. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. There are 9 sides, so this is a nonagon. Lines containing some of the sides will pass through the interior of the nonagon, so it is concave. Since the polygon is concave, it must be irregular. Answer: nonagon, concave, irregular

Assignment 1-6 Page 61, 1-5, 11-16 You should have three answers for 1-2, 11-16. Name by the number of sides Convex or concave Regular or irregular