1. Section 3-5: The Polygon Angle-Sum Theorem

2. Objectives To classify polygons. To find the sums of the measures of the interior and exterior angles of a polygon.

3. Vocabulary Polygon Convex Polygon Concave Polygon Equilateral Polygon Equiangular Polygon Regular Polygon

4. Polygon A polygon is a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints and no adjacent sides are collinear.

5. Are the following figures polygons?

6. Naming a Polygon

7. Classification of Polygons by Sides Number of SidesName of Figure 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon

8. Convex Polygon A convex polygon has no diagonal with points outside the polygon.

9. Concave Polygon A concave polygon has at least one diagonal with points outside the polygon.

10. Classify each Polygon Classify each polygon by its sides. Identify the polygon as convex or concave.

11. Theorem 3-14: “Polygon Angle Sum Theorem” The measures of the angles of an n-gon is:

12. Finding a Polygon Angle Sum Find the sum of the measures of the angles of a 15-gon.

13. Using the Polygon Angle-Sum Theorem Solve for x.

14. Theorem 3-15: “Polygon Exterior Angle-Sum Theorem” The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360º.

15. Equilateral Polygon An equilateral polygon has all sides congruent.

16. Equiangular Polygon An equiangular polygon has all angles congruent.

17. Regular Polygon A regular polygon is both equilateral and equiangular.

18. Example Find the measure of an interior angle and an exterior angle of a regular octagon.