10 1 Polygons Objectives To identify and name

10 -1 Polygons Objectives: • To identify and name polygons. • To find the sum of the measures of interior and exterior angles of convex polygons and measures of interior and exterior angles of regular polygons. • To solve problems involving angles measures of polygons.

Vocabulary • • • Polygon Convex Concave N-gon Regular Polygon

Definition of Polygon • A polygon is a closed figure formed by a finite number of coplanar segments such that: 1. the sides that have a common endpoint are noncollinear, and 2. each side intersects exactly two other sides, but only at their endpoints.

Convex • A Convex Polygon is a polygon that has all interior angles less than 180°. Thus resulting in all the vertices pointing “outwards”, away from the center.

Concave • A Concave Polygon is a polygon that has one or more interior angles greater than 180°. Thus resulting in some vertices “point inwards” towards the center.

n-gon

Regular Polygon • A regular polygon is a convex polygon with all sides congruent and all angles congruent.

Theorem 10 -1 Interior Angle Sum Theorem • If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S = 180(n – 2).

Theorem 10 -2 Exterior Angle Sum Theorem • If a polygon is convex, the sum of the measures of the exterior angles, one at each vertex, is 360°.

In Class Examples

Homework 10 -1 Worksheet