1. 6-1B Exploring Polygons How are polygons classified? How are polygons classified? How do you find the sum of the measures of the interior angles of a convex polygon? How do you find the sum of the measures of the interior angles of a convex polygon? What is the sum of the measure of the exterior angles of a convex polygon? What is the sum of the measure of the exterior angles of a convex polygon?

2. Definitions A polygon is a plane figure whose sides are three or more coplanar segments that intersect only at their endpoints (the vertices). Consecutive sides cannot be collinear, and no more than two sides can meet at any one vertex. A polygon is a plane figure whose sides are three or more coplanar segments that intersect only at their endpoints (the vertices). Consecutive sides cannot be collinear, and no more than two sides can meet at any one vertex.

3. Definition A diagonal of a polygon is a line segment whose endpoints are any two nonconsecutive vertices of the polygon. A diagonal of a polygon is a line segment whose endpoints are any two nonconsecutive vertices of the polygon.

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

5. Convex Polygons

6. Concave Polygons

7. Not Polygons

8. Classification of Polygons 3sides Triangle 4sides Quadrilateral 5sides Pentagon 6sides Hexagon 7sides Heptagon 8sides Octagon 9sides Nonagon 10 sides Decagon 12 sides Dodecagon 20 sides Icosagon See page 403 for chart

9. Try It Name the polygon Name the polygon Classify the polygon Classify the polygon How many diagonals can be drawn from vertex A? How many diagonals can be drawn from vertex A? Is the polygon concave or convex? Is the polygon concave or convex? AB C D E F

10. Polygon interior angles What happens to the sum of the degrees of the inside angles as the number of sides increases? 180°360° 540° 720° Is there an easier way to figure out the sum of the degrees of the inside angles for any polygon?

11. Angle-Sum Theorem for Polygons The sum of the measures of the interior angles of a convex polygon with n sides is given by S = (n − 2)180°

12. Polygon exterior angles What happens to the sum of the degrees of the outside angles as the number of sides increases? 360° Is there an easier way to figure out the sum of the degrees of the outside angles for any polygon?

13. Exterior Angle Theorem for Polygons The sum of the measures of the exterior angles of a convex polygon (one at each vertex) is 360°

14. Find the sum of the interior angles and exterior angles for the polygon 7 sidesHeptagon Interior angle sum = (n − 2)180° = (7 − 2)180° = (7 − 2)180° = (5)180° = (5)180° = 900° = 900° Exterior angle sum = 360°

15. Find the sum of the interior angles and exterior angles for the polygon 22-gon Interior angle sum = (n − 2)180° = (22 − 2)180° = (22 − 2)180° = (20)180° = (20)180° = 3600° = 3600° Exterior angle sum = 360°

16. How are polygons classified? How are polygons classified? Polygons are classified by the number of sides. How do you find the sum of the measures of the interior angles of a convex polygon? How do you find the sum of the measures of the interior angles of a convex polygon? S = (n −2)180° What is the sum of the measure of the exterior angles of a convex polygon? What is the sum of the measure of the exterior angles of a convex polygon? 360° 360°

17. Assignment 6-1B Page 406, 1-3, 6-12, 25-26, 31-35