Polygons and Angles Sec 12 -1E pg. 693 - 698

Definition Polygon – a simple, closed figure formed by three or more straight line segments. A polygon is named by the letters of its vertices, written in consecutive order. Not Polygons Polygons

Polygons – or Not? Polygons have Not Polygons Line segments are called sides Sides meet only at their endpoints Points of intersection are called vertices Not Polygons Figures have sides that cross each other Figures are open Figures have curved sides. Not Polygons Polygons

Regular Polygons An equilateral polygon has all sides congruent. A polygon is equiangular if all of its angles are congruent. A regular polygon is equilateral and equiangular with all sides and all angles congruent.

Names of Polygons Number of Sides Name 3 Triangle 4 Quadrilateral 5 6 7 8 9 10 12 n sides Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon An 11 sided polygon is sometimes referred to as a undecagon or a hendecagon

Interior Angle Sum of a Polygon The sum of the measures of the angles of a polygon is given by S = 180 (n – 2) Where n represents the number of sides. The sum of the interior angles is 540 n = 5 S = 180 (n – 2) S = 180 (5 – 2) = 180 (3) S = 540

Work this problem Find the sum of the measures of the interior angles of this polygon. This is a hexagon, so it has 6 sides. S = 180 (n – 2) What is the measure of an individual interior angle? S = 180 (6 – 2) S = 180 ( 4) The measure of an individual interior angle is 720/6 = 120 S = 720