1. Section 3-5 Angles of Polygons
Objective:
Recognize and name the convex polygons and regular polygons.
Find the measures of the interior angles and exterior angles of convex polygons.
Standard 2.9 Concepts in Geometry

2. The left five figures are polygons. The right figures are not
The left five figures are polygons. The right figures are not. Using this knowledge, write the definitions or qualities a polygon can/cannot have.

3. Polygons Made up of segments (thus no curves)
Must have three or more sides
Can be non-convex but we focus on convex.
Ex. Non-Convex where there is at least one line that is interior

4. Convex vs. Non-Convex

5. Naming Polygons Number of Sides Name 3 Triangle 4 Quadrilateral 56 8 10 n
Name
Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
Decagon
n-gon

6. How many different triangles can be forms by drawing diagonals through the following polygons Definition of diagonal: interior segment from one vertex to another.
4 sides & 2 triangles
6 sides & 4 triangles
3 sides & 1 triangles
8 sides & 6 triangles

7. Investigation-Fill in the chart and make a conjecture: #of sides #of angle sum n

8. Theorem 3-13 The sum of the measures of the angles of a convex polygon with n sides is (n-2) 180
Interior Angle Thm

9. Exterior Angle Sum Theorem
Theorem 3-14 The sum of the measures of the exterior angles of any convex polygon, one angle at each, is 360
Exterior Angle Sum Theorem

10. Ex. If a polygon has 22 sides. Find the interior and exterior angle sum.
Interior sum
(n-2) 180
(22-2) 180
(20) 180
3600
Exterior sum
360

11. Regular Polygons Regular polygons are equiangular and equilateral.
Thus all their interior angles are ______ and all their sides are _______.

12. Example 1
All regular 7 sided figures have interior angle measures of ____ and exterior angle measures of _____.
Answers: int = ext = 51.5

13. Example 2
All regular 6 sided figures have interior angle measures of ____ and exterior angle measures of _____.
Answers: int = 120° and ext = 60°.

14. Group Work
CE p. 103 #1-6 and 9 HW
WE p.104 #1-23 all