1. Lesson 3-4: Polygons 1 Polygons

2. Lesson 3-4: Polygons 2 These figures are not polygonsThese figures are polygons Definition:A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.

3. Classifications of a Polygon Lesson 3-4: Polygons 3 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. Classifications of a Polygon Lesson 3-4: Polygons 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.

5. Polygon Names Lesson 3-4: Polygons 5 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

6. Convex Polygon Formulas….. Lesson 3-4: Polygons 6 Diagonals of a Polygon: For a convex polygon with n sides: The sum of the interior angles is A segment connecting nonconsecutive vertices of a polygon The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is

7. 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 5.The number of sides of regular polygon with interior angle 172 ° is Examples….. Lesson 3-4: Polygons 7