Polygons and Angles Lesson 3 Pg 27 Key

Polygons and Angles Lesson #3 Pg. 27

Key Vocabulary • Polygon – A simple, closed figure formed by three or more line segments • Equilateral – A polygon in which all the sides are congruent • Equiangular – A polygon in which all the angles are congruent • Regular Polygon – A polygon that is both, equilateral and equiangular

Polygons you Should KNOW. . Number of Sides Name of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Hendecagon 12 Dodecagon

Interior Angle Sum of a Polygon • The sum (S) of the measures of the interior angles of a polygon is (n – 2) 180, where n represents the number of sides in the polygon • HINT: A triangle has 180° in interior angles, from one vertex in the polygon connect line segments to the other vertices to see how many triangles are created. • Multiply the amount of triangles by 180

Examples of Interior Angles in Polygons Number of Sides (n) 3 4 5 6 Sketch of Figure Number of Triangles Sum of Angle Measure (n-2)180 1 1(180°)=180°

Examples • Find the sum of the measures of the interior angles of a decagon. • Hexagon? • Octagon? • 15 -gon?

Examples • Each chamber of a bee honeycomb is a regular hexagon. Find the measure of an interior angle (1) of a regular hexagon. • Octagon? • Heptagon? • 20 -gon?

Exterior Angles of a Polygon • In a polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 2 1 1 3 5 4 5 2 4 3

Examples • Find the measure of an exterior angle in a regular hexagon. • Triangle? • Quadrilateral? • Octagon?

Homework • HC: pg. 31 -32 (1 -15) • CC: pg. 31 -32 (1 -7, 9, 11, 14, 15)