Section 2.5 Convex Polygons A polygon is a closed plane figure whose sides are line segments that intersect only at the endpoints. Convex polygons angles are between 0 and 180 Concave polygons have one angle that is more than 180 (reflex angle) Fig. 2.29 p. 99 5/5/2019 Section 2.5 Nack

Types of Polygons Polygon Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 5/5/2019 Section 2.5 Nack

Diagonals of a Polygon Definition: a line segment that joins two nonconsecutive vertices. Theorem 2.5.1: The total number of diagonals D in a polygon of n sides is given by the formula: Polygon Number of Diagonals Triangle Quadrilateral 2 Pentagon 5 Hexagon 9 Heptagon ? 14 Octagon ? 20 Nonagon ? 27 Decagon ? 35 5/5/2019 Section 2.5 Nack

Sum of the Interior Angles of a Polygon Sum of Interior Angles Triangle 180 Quadrilateral 360 Pentagon 540 Hexagon 720 Heptagon 900  Octagon 1080  Nonagon 1260  Decagon 1440  Theorem 2.5.2: The sum S of the measures of the interior angles of a polygon with n sides is given by S = (n-2) 180 5/5/2019 Section 2.5 Nack

Regular Polygons A polygon that is both equilateral and equiangular Corollary 2.5.3: The measure l of each interior angle of a regular polygon or equiangular polygon of n sides is: Corollary 2.5.4: The sum of the four interior angles of a quadrilateral is 360. Corollary 2.5.5: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. Proof p. 104 Corollary 2.5.6: The measure E of each exterior angle of a regular polygon or equiangular polygon in n sides is E = 360/n Ex. 6 p. 104 Polygrams: Figure created when sides of a convex polygon are extended. Fig. 2.37 p. 109 5/5/2019 Section 2.5 Nack