1. Chapter 3 Lesson 4 Objective: Objective: To classify polygons.

2. Polygon: Polygon: 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. A B C DE A B C D E A B C DE A polygon Not a polygon; not a closed figure Not a polygon; two sides intersect between endpoints

3. Example 1: Naming a Polygon verticessides angles Name the polygon. Then identify its vertices, sides, and angles. A B C DE To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction. Two names for this polygon are ABCDE and CDEAB. Vertices: Vertices: A,B,C,D,E Sides: Sides: AB, BC, CD, DE, EA Angles: Angles: A, B, C, D, E

4. Example 2: Naming a Polygon Three polygons are pictured. Name each polygon, its sides and its angles. A B C D E Sides: Sides: BC, CD, DE, EB Name: Name: BCDE Angles: Angles: B, C, D, E Name: Name: ABE Sides: Sides: AB, BE, EA Angles: Angles: A, B, E Name: Name: ABCDE Sides: Sides: AB, BC, CD, CE, EA Angles: Angles: A, B, C, D, E

5. You classify a polygon by the number of sides it has. SidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon

6. Convex polygon: Convex polygon: has no diagonals with points outside the polygon. AB C D E Diagonals

7. Concave polygon: Concave polygon: has at least one diagonal with points outside the polygon. A B CD E F G

8. Example 3: Classify each polygon by its sides. Identify each as convex or concave. a. Hexagon;Convex b. Octagon;Concave

9. Theorem 3-9: Polygon Angle-Sum Theorem (n-2)180 The sum of the measures of the angles of n-gon is (n-2)180. Example 4: Find the sum of the measures of the angles of a 15-gon. For a 15-gon, n = 15 Sum = (n – 2)180 (15 – 2)180 13180 2340 Polygon Angle-Sum Theorem Substitute Simplify

10. Example 5: Finding a Polygon Angle Sum Find the sum of the measures of the angles of a decagon. 10 Decagon = 10 (n-2)180 (10-2)180 8180 1440

11. Theorem 3-10: Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. 1 234 5 For the pentagon, m 1 + m 2 + m 3 + m 4 + m 5 = 360.

12. Example 6: Finding Exterior Angles of a Polygon 80° 150° x° 80+150+x=360 230+x=360 x=130

13. Equilateral Polygon: Equilateral Polygon: all sides congruent. Equiangular Polygon: Equiangular Polygon: all angles congruent. Regular Polygon: Regular Polygon: is both equilateral and equiangular.

14. Homework Page 147 – 149 #1-25; 32 – 35; 47 - 49