Lesson 3-4 Polygons

A polygon is a closed figure No, not a polygon Yes, a polygon

A polygon formed by a finite number of coplanar segments No, not a polygon Yes, a polygon

No, not a polygon Yes, a polygon A polygon has segments that intersect exactly two other sides, but only at their endpoints. No, not a polygon Yes, a polygon

Definition of a Polygon A closed figure formed by a finite number of coplanar segments such that the segments intersects exactly two other sides, but only at their endpoints.

Classifications of a Polygon Convex Concave Regular Irregular

Convex Polygon No line containing a side of the polygon contains a point in its interior

(think the opening of a cave) Concave Polygon the opposite of convex (think the opening of a cave)

Regular Polygon A convex polygon in which all angles have the same measure and all sides are the same length

Two sides (or two interior angles) are not congruent Irregular Polygon Two sides (or two interior angles) are not congruent

Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon Dodecagon 12 sides n sides n-gon

a segment connecting nonconsecutive vertices of a polygon Diagonals of a Polygon a segment connecting nonconsecutive vertices of a polygon

For a convex polygon with n sides: The sum of the interior angles is The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is