1. Objectives To identify and name polygons To find the sum of the measures of interior and exterior angles of convex and regular polygons To solve problems involving angle measures of polygons

2. Polygon A polygon is a closed figure formed by a finite number of coplanar segments such that the sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their endpoints

3. Examples are

4. Convex Polygon A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. Examples are

5. Concave Polygon A concave polygon is a polygon such that the lines containing a side of the polygon contains a point in the interior of the polygon. Examples are

6. A n-gon is a polygon with n sides Number of SidesPolygon 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon 11Hendecagon 12Dodecagon Nn-gon

7. Regular Polygon A regular polygon is a convex polygon with all sides and angles congruent

8. Theorems

9. Interior Angle Sum Theorem If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S = 180(n – 2) Find the sum of a convex polygon that has 3 sides S = 180(3 – 2) S = 180 Find the measure of each interior angle of a regular hexagon First find the sum of all of the angles in the hexagon S = 180(6 – 2) S = 720 Then to find the measure of each interior angle, divide the sum of the angles by the number of angles in the hexagon 720/6 or 120

10. Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360 Use the Exterior Angle Sum Theorem to find the measure of an interior angle and an exterior angle of a regular polygon A regular polygon has 5 congruent interior angles. So the measure of each exterior angle is 360/5 or 72 Because each exterior angle is supplementary to each interior angle the measure of each interior angle is 180 – 2 or 108

11. Homework!

12. pp. 519-520 Problem numbers 22-56 even