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11.1-Polygon Basics polygon “poly” = many…and “gon” = sides So a polygon is a closed shape with 3 or more sides. Examples: Triangle Rectangle Hexagon

Every polygon has the same features: 11.1-Polygon Basics Every polygon has the same features: Sides – at least 3 sides made of straight line segments Vertices (aka endpoints) – connects the sides and forms <s Angles – at least 3 <s with varying degrees (each less than 180°)

11.1-Polygon Basics # of Sides Type of Polygon Pic of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

11.1-Polygon Basics Special Terms for Polygons: Convex – no line of a side contains a point inside the polygon Concave (aka nonconvex) – line of a side contains a point inside the polygon Regular Polygon – convex polygon that is both equilateral and equiangular Consecutive Vertices – endpoints that are on same side (back-to-back) Diagonal – segment that joins 2 nonconsecutive vertices

Interior Angles Theorem 11.1-Polygon Basics Interior Angles Theorem The sum of the interior angles of a convex n-gon is: (n-2) * 180° Example: Find the sum of the angles in the figure: Octagon

Example: Find the value of x in the figure: 11.1-Polygon Basics Example: Find the value of x in the figure: 108° 121° Quadrilateral x° 59°

11.1-Polygon Basics Example: The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides.

11.1-Polygon Basics Exterior Angles Theorem The sum of the exterior angles of a convex n-gon is: m<1 + m<2 + … + m<n = 360° Example: Find the value of x in the figure below: 86° x 90° 3x