CCSS G-CO 9: Prove theorems about lines and angles. G-CO 10: Prove theorems about triangles. G-CO 11: Prove theorems about parallelograms. Lesson Goals Identify, name, and describe polygons. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers a 2-dimensional plane figure Formed by three or more line segments called sides Adjacent sides are non-collinear Each side intersects exactly 2 other sides at their endpoints polygon MNOPQR polygons are named using the vertices in consecutive order yes no Which of the shapes are polygons? triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n-gon Convex No line that contains a side passes through the interior of the polygon interior Convex All vertices point outward. Convex No line that contains a side passes through the interior of the polygon Concave A polygon that is not convex interior Concave At least one vertex points inward. Not a polygon Some sides are not line segments Is the figure a polygon? If it is, state whether it is convex or concave. Classify by number of sides. octagon Convex or Concave? concave Classify by number of sides. dodecagon Convex or Concave? convex Classify by number of sides. heptagon Convex or Concave? concave Equilateral: all sides congruent Equiangular: all angles congruent Regular: equilateral and equiangular State whether the polygon is best described as equilateral, Equiangular, regular, or none of these? regular equilateral equilangular The sum of the measures of the interior angles of a convex polygon is where n is the number of sides Find the sum of the measures of the interior angles of a convex decagon. Find x. Find the value of x. Find the measure of each interior angle. Is the quadrilateral regular? D B C A Not regular A polygon is __________________. A polygon is classified by _________, _________, or ________. A regular polygon has _____________. The Polygon Interior Angle Sum Theorem says ____________. p. 325: 1, 2, 4 9, , 27 32, 41 45 o p. 665: 3, 4, 7, 13, 15, 20, 49