1. The Polygon Angle- Sum Theorems

2. What is a Polygon???
Polygon
A polygon is a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.
Not a Polygon
not closed
Not a Polygon
two sides intersect between endpoints

3. How To Name a Polygon
To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction.

4. Naming Polygons
Name the polygon. Then identify it’s vertices, sides, and angles.
Two names for this polygon are DHKMGB and MKHDBG.
Vertices: D,H,K,M,G,B
Sides: DH, HK, KM, MG, GB, BD
Angles: D, H, K, M, G, B B D H G M K

5. How are polygons classified
How are polygons classified??? -Polygons are classified as convex or concave A D R T Y
Diagonal W M P K G S Q
A convex polygon has no diagonal with points outside the polygon.
A concave polygon has at least one diagonal with points outside the polygon.

6. Classifying polygons continued…
Sides
Name 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
n-gon

7. An n-gon is a polygon with n sides, where n can be 3, 4, 5, 6,……..
Vocabulary Tip
An n-gon is a polygon with n sides, where n can be 3, 4, 5, 6,……..

8. Polygon Angle-Sum Theorem
The sum of the measures of the
angles of an n-gon is (n-2)180.

9. Finding a Polygon Angle Sum
Find the sum of the measure of the angles of a 15-gon.
For a 15-gon,n=15
Sum = (n-2)180 POLYGON ANGLE-SUM THEOREM
= (15-2)180 SUBSTITUTE.
= 13(180) SIMPLIFY
= 2340
*The sum of the measures of the angles of a 15-gon is 2340*

10. Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
For the pentagon,
m<1+ m<2+ m<3+ m<4+ m<5 =360 5 4 1 2 3

11. Vocabulary
An equilateral polygon has all sides congruent. An Equiangular polygon has all angles congruent. A regular polygon is both equilateral and equiangular.