 A polygon is a closed lane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear. A D C B A B C D E A B C E D E POLYGON NOT A POLYGON NOT A CLOSED FIGURE SIDES INTERSECT

 Polygons have vertices, sides, and angles  Vertices: a point where two segments meet  Each vertex is also an angle  Sides are in between two vertices.  To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counter clockwise direction.

 Name the polygon, then identify its vertices, sides, and angles.  Vertices:  Sides:  Angles: B G M K HD

 You can classify polygons by the number of sides it has.

 Polygons can also be classified as convex or concave. A R TY D All the vertices of the polygon will point outward, away from the inside of the polygon W K S Q G PM CONVEX CONCAVE A vertex that is pushed in towards the inside of the polygon. The polygon “caves” in.

 Classify each polygon by the number of sides and identify if it is concave or convex.

PolygonNumber of SidesNumber of Triangles Formed Sum of the Interior Angles

 Find the measure of the angles of a 15-gon.

 Find m ∠ y. M VY R T

 3-10 Polygon Exterior Angle-Sum Theorem › The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360° › For the pentagon m ∠ 1 + m ∠ 2 + m ∠ 3 +m ∠ 4 + m ∠ 5 = 360°

 An equilateral polygon has all sides congruent.  An equiangular polygon has all angles congruent.  A regular polygon is both equilateral and equiangular.

 Find the measure of each given the figure is a regular polygon. a. Sum of the interior angles b. The measure of 1 interior angle c. The sum of the exterior angles d. The measure of 1 exterior angle

 The sum of the measure of the angles of a polygon is 4,500. Find how many sides the figure has.

 The measure of an exterior angle of a regular polygon is 40°. Find the measure of an interior angle, and the number of sides.

 Pg  1-25, 32-35