Polygons Sec: 6.1 Sol: G.10

Definition of Polygon A polygon is a closed figure formed by an finite number of coplanar segments such that the sides that have a common endpoint are non-collinear each side intersects exactly two other sides, but only at their endpoints. Symbolic Representation: Is named by the letters of it’s vertices, in consecutive order.

A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is called concave.

Polygons may be classified by the number of sides they have Polygons may be classified by the number of sides they have. In general, a polygon with n sides is called an n-gon. This means the nonagon can also be called a 9-gon. Polygon Number of Sides Polygon 3 triangle 4 5 6 7 8 9 10 12 n

Perimeter Triangle Square Rectangle Is the sum of the lengths of its sides. Perimeter of Special shapes: Triangle Square Rectangle

Find the Perimeter

Find the Perimeter using the coordinate plane: P(-5, 1), Q(-1, 4), R(-6, -8) Step 1: Graph the points. Step 2: Use distance formula on all sides. Step 3: Add the three sides.

Regular polygon a convex polygon with all angles and all sides congruent.

Diagonal of a polygon a segment drawn from one vertex of a polygon to a nonconsecutive vertex.

Notice in each case before this the polygon is separated into triangles. The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of the triangles. This is easy to find since the sum of the angles in a triangle = ______. Use the chart below to find a pattern: Convex Polygon # of sides # of triangles Sum of  measures triangle 3 1 1(180) = 180 quadrilateral 4 2 2(180) = 360 pentagon hexagon heptagon octagon n-gon

Interior Angle Sum Theorem If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S = 180(n – 2).

Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360.

Consider the following regular polygons Consider the following regular polygons. Find the sum of the exterior angles

Find the sum of the measures of the interior angles of each convex polygon: 1. decagon 2. 21-gon 3. 13-gon 4. 46-gon The measure of an exterior angle of a regular polygon is given. Find the number of sides of the polygon. 5. 30 6. 8 7. 72 8. 14.4

The number of sides of a regular polygon is given The number of sides of a regular polygon is given. Find the measures of an interior angle and an exterior angle for each polygon. Round to the nearest hundredth 9. 30 10. 9 11. 22 12. 14 The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon. 13. 135 14. 144 15. 176.4 16. 165.6

Find the measure of each interior angle

Suggested Assignments Classwork: WB pg147-148 2-56 even Homework: Pg 356-357 7-25, 29, 30, 32, 33