Section 3-5: The Polygon Angle-Sum Theorem

1. Chapter 3: Parallel and Perpendicular Lines 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

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.