Math Humor Q: What type of figure is like a lost parrot? A: A polygon!!

LT 6.1: Apply Properties and Attributes of Polygons

Number of Sides Name of Polygon 3 How many do you know? 4 5 6 7 8 9 10 11 12 n

Number of Sides Name of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon 12 Dodecagon n n-gon

Identifying Polygons Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.

Classifying Polygons Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.

Sum of Interior Angle Measures Polygon Number of Sides Number of Triangles Sum of Interior Angle Measures Triangle 3 1 (1) 180˚ = 180˚ Quadrilateral 4 2 (2) 180˚ = 360˚ Pentagon 5 (3) 180˚ = 540˚ Hexagon 6 (4) 180˚ = 720˚ n-gon n n – 2 (n - 2) 180˚

Polygon Angle Sum Theorem The sum of the interior angle measures of a convex polygon with n sides (n – 2) x 180˚.

Example Find c 8c = 360 c = 45 P R S Q c˚ 3c˚

Polygon Exterior Angle Sum Theorem The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360˚.

Example Find the angles 18a = 360 a = 20 140°, 60°, 120°, 40°

Example Find the following for a regular convex nonagon: Sum of the interior angles 1260° Each interior angle 140° Sum of the exterior angles 360° Each exterior angle 40°