6.1 Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons. Side of a polygon Vertex of a polygon Diagonal Regular polygon Concave convex Polygon Angle Sum Theorem Polygon Exterior Angle Sum Theorem

Number your paper 1. 2. 3. 4. 5. 6.

Classifying polygons by number of sides. 1 2 3 4 5 6 See text!

A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. Concave: any diagonal passes outside of the polygon Convex:no diagonal passes outside the polygon regular irregular

Number your paper 1. 2. 3. 4. 5.

Tell whether each polygon is regular or irregular and concave or convex. 1 2 5 4 3

Draw these! 1. 2. 3. 4. 5.

Sketch! convex, irregular hexagon concave triangle. Examples: Sketch a polygon that meets each of the following characteristics, if possible. Sketch! convex, irregular hexagon concave triangle. Regular quadrilateral convex nonagon concave, regular pentagon

Find the sum of the interior angle measures of each convex polygon by drawing all possible diagonals from one vertex of the polygon. How does the triangle sum theorem help you?

Work it! Example 1: Find the sum of the interior angle measures of a convex heptagon.

Work it! Example 2: Find the measure of each interior angle of pentagon ABCDE.

Talk about it! How would you calculate the measure of each interior angle of a regular decagon? What if it’s not regular?

Handbook page 19 Interior Angles Exterior Angles Sum of all angles Measure of one if the polygon is REGULAR!

Talk about it! What is the measure of each interior angle of a regular decagon? What is the measure of each exterior angle of a regular decagon? What is the SUM of all of the exterior angles?

Watch it! In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.

Angle measures of a convex polygon with n sides Interior Angles Exterior Angles Sum of all angles Measure of one if the polygon is REGULAR!

Work it! Example 3: Find the value of b in polygon FGHJKL.

Work it! Example 4 Find the measure of each exterior angle of a regular 20-gon.

Talk about it! Ann is making paper stars for party decorations. If the pentagon in the center of the star is regular, what is the measure of 1? 2? 2