6 1 Polygons Targets Identify name and describe

6. 1 Polygons

Targets: • Identify, name, and describe polygons. • Find and Use the sum of the measures of the interior angles of a polygon. • Find and Use the sum of the measures of the exterior angles of a polygon.

Definitions: SIDE • Polygon—a plane figure that meets the following conditions: – It is formed by 3 or more segments called sides, such that no two sides with a common endpoint are collinear. – Each side intersects exactly two other sides, one at each endpoint. • Vertex – each endpoint of a side. Plural is vertices. You can name a polygon by listing its vertices consecutively. For instance, PQRST and QPTSR are two correct names for the polygon above.

Example 1: Identifying Polygons • State whether the figure is a polygon. If it is not, explain why. • Not D – has a side that isn’t a segment – it’s an arc. • Not E– because two of the sides intersect only one other side. • Not F because some of its sides intersect more than two sides/ Figures A, B, and C are polygons.

Polygons are named by the number of sides they have – MEMORIZE Number of sides Type of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon

Polygons are named by the number of sides they have – MEMORIZE Number of sides Type of Polygon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

Convex or concave? • Convex if no line that contains a side of the polygon contains a point in the interior of the polygon. • Concave or non-convex if a line does contain a side of the polygon containing a point on the interior of the polygon. See how this crosses a point on the inside? Concave. See how it doesn’t go on the Inside-- convex

Convex or concave? • Identify the polygon and state whether it is convex or concave. A polygon is EQUILATERAL If all of its sides are congruent. A polygon is EQUIANGULAR if all of its interior angles are congruent. A polygon is REGULAR if it is equilateral and equiangular.

Identifying Regular Polygons • Remember: Equiangular & equilateral • Decide whether the following polygons are regular. Equilateral, but not equiangular, so it is NOT a regular polygon. Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon. Pentagon is equilateral and equiangular, so it is a regular polygon.

Angles of Polygon Laws • Sum of the Interior angles of a convex Polygon = (n - 2) 180, where n = # of sides of the polygon • Sum of the Exterior angles of a convex polygon = 360. • One interior angle of a regular polygon = [(n -2) 180] / n, where n = # of sides