1. 1 1-29-15 Unit 8 Polygons and Quadrilaterals Polygons

2. 2 These figures are not polygonsThese figures are polygons Definition:A closed figure formed by coplanar segments so that each segment intersects exactly two others, but only at their endpoints. Polygons

3. 3 Classifications of a Polygon Convex:No line containing a side of the polygon contains a point in its interior Concave: A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.

4. 4 Regular:A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular: Two sides (or two interior angles) are not congruent. Classifications of a Polygon Diagonals of a Polygon: A segment connecting nonconsecutive vertices of a polygon

5. Interior angle: An angle formed by two adjacent sides inside the polygon. Exterior angle: An angle formed by two adjacent sides outside the polygon. Polygons Angles of a Polygon

6. Interior angle Exterior angle Polygons

7. 7 Polygon Names 3 sides Triangle 4 sides 5 sides 6 sides 7 sides 8 sides Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral 10 sides 9 sides 12 sides Decagon Dodecagon n sides n-gon

8. 8 Convex Polygon Formulas….. For a convex polygon with n sides: The sum of the interior angles is The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is

9. 9 Examples….. 1.Sum of the measures of the interior angles of a 11-gon is (n – 2)180°  (11 – 2)180 °  1620 2.The measure of an exterior angle of a regular octagon is 3.The number of sides of regular polygon with exterior angle 72 ° is 4.The measure of an interior angle of a regular polygon with 30 sides