1. Is it too much to ask for a LITTLE PRECIPITATION?! -Evan Lesson 4: (3.5) The Polygon Angle-Sum Theorems LT: To classify polygons and to find the measures of the angles of a polygon.

2. Classifying Polygons Polygon: Closed plane figure with at least three sides that are segments intersecting only at their endpoints, and no adjacent sides are collinear. A B C D E A B C D E A B C D E Not a polygon Polygon

3. Classifying Polygons Note: A diagonal of a polygon is a segments that connects two nonconsecutive vertices. Convex Polygon: A polygon with no diagonal with points outside the polygon Concave Polygon: A polygon with at least one diagonal with points outside the polygon. Convex Concave

4. Classifying Polygons We can classify polygons according to the number of sides it has. Sides Name 3 4 5 6 8 9 10 12 n Triangle Quadrilateral Pentagon Hexagon Octagon Nonagon Decagon Dodecagon n-gon

5. Classifying Polygons Classify each polygon by its sides. Identify each as convex or concave.

6. Classifying Polygons Equilateral Polygon: A polygon with all sides congruent. Equiangular Polygon: A polygon with all angles congruent. Regular Polygon: A polygon that is both equilateral and equiangular.

7. Naming Polygons C D G H J K F Vertices: Sides: Angles: Polygon:

8. Super Fun Activity!  Sketch polygons with 4, 5, 6, 7, and 8 sides on chart paper  Divide into triangles by drawing diagonals from one vertex  Multiply the # of Δ’s by 180 to find the polygon angle-sum # of Sides# of Δ’s FormedAngle-Sum 4 5 6 7 8 Theorem 3-14: Polygon Angle-Sum Theorem: The sum of the measures of the angles in an n-gon is (n – 2)180. n

9. Polygon Angle Sums Find the sum of the measures of the angles of a regular dodecagon. Then find the measure of an interior angle. The sum of the angles of a polygon is 720. Find the number of sides the polygon has and classify it.

10. Polygon Angle Sums Find x in the following polygon. 125° x°x°

11. Polygon Angle Sums Theorem 3-15: Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For a pentagon: 1 2 3 4 5

12. Polygon Angle Sums If the measure of an exterior angle of a regular polygon is 30, find the number of sides and classify it.

13. (3.5) The Polygon Angle-Sum Theorems It took me like three hours to finish the shading on your upper lip. It's probably the best drawing I've ever done. -Napoleon HOMEWORK: (3.5) Pgs. 161-162; #2-26 even, 32, 34, 40,42 TERMS: Polygon, Convex Polygon, Concave Polygon, Equilateral Polygon, Equiangular Polygon, Regular Polygon