3-5 The Polygon Angle-Sum Theorems SWBAT: Classify polygons Find the sums of the measures of the interior and exterior angles of polygons

Polygon: closed plane figure with at least 3 sides that are segments; the sides intersect only at their endpoints, and no adjacent sides are collinear

To name a polygon, start with any vertex and list the vertices consecutively in a clockwise or counterclockwise direction. What are the different ways you can name this polygon? ABCDE EABCD DCBAE BCDEA and many more…

Diagonal: a segment that connects two nonconsecutive vertices Name the diagonals below. a) b)

You can classify a polygon by the number of sides it has You can classify a polygon by the number of sides it has. Here are some common polygon names:

Polygons are classified as convex or concave. A convex polygon has no diagonal with points outside the polygon. A concave polygon has at least one diagonal with points outside the polygon.

Example 1: Classify each polygon by its sides Example 1: Classify each polygon by its sides. Identify each as convex or concave.

You try. c) d) c) Octagon; concave d) quadrilateral; convex

Polygon Angle Sum Theorem

Example 3: The sum of the measures of the angles of a given polygon is 720. How can you find the number of sides in the polygon?

Example 4

Try this.

Think about this one… Pentagon ABCDE has 5 congruent angles Think about this one… Pentagon ABCDE has 5 congruent angles. Find the measure of each angle. This is the Sum of All Angles! How many angles are there in total? How would we find one?

A little more terminology… Find the measure of an exterior angle for a regular decagon.

You can draw exterior angles at any vertex of a polygon You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of the exterior angles, one at each vertex, is 360.

The sum of the exterior angles of any polygon is 360, so what polygon has its interior angles sum to 360?