Polygons and Angles Sec 12 1 E pg

Polygons and Angles Sec 12 -1 E 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 – or Not? • Polygons have – 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

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 • 3 • 4 • 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. n=5 S = 180 (n – 2) S = 180 (5 – 2) = 180 (3) S = 540 The sum of the interior angles is 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) S = 180 (6 – 2) S = 180 ( 4) S = 720 What is the measure of an individual interior angle? The measure of an individual interior angle is 720 /6 = 120