1. Ms. Jennifer Swanson & Ms. Amanda Phifer
Polygons
Ms. Jennifer Swanson
&
Ms. Amanda Phifer

2. What is a polygon?
A Polygon is a shape that is a closed plane figure where
All line segments are straight
Lines don’t cross or use end points more than once
Only consists of outer shape, not inner area
Regular Polygons are EQUILATERAL and EQUANGULAR

3. A regular polygon… All angles and sides are equal!
If not, then is irregular
Vertices are corner points on a polygon.
Irregular
Regular

4. Angles Angles total greater than 180 degrees
Convex
Concave
Angles total greater than 180 degrees
Has reflex angles
Caves in
Angles total to 180 degrees or less
Flex out

5. What do polygons look like?

6. 360 degree angles Total, 90 deg. each
Triangle
Quadrilateral
4 sided figure, 4 angles
360 degree angles Total, 90 deg. each
4 vertices, 1 diagonal from single vertex
3 sided figure, 3 angles
180 deg. angles Total, 60 deg. each
3 vertices, 0 diagonals from single vertex

7. 540 deg. angles Total, 108 deg. each
Pentagon
Hexagon
5 sided figure, 5 angles
540 deg. angles Total, 108 deg. each
5 vertices, 2 diagonals from single vertex
6 sided figure, 6 angles
720 deg. angles Total, 120 deg. each
6 vertices, 3 diagonals from single vertex

8. 900 deg. angles Total, 128.57 deg. each
Heptagon
Octagon
7 sided figure, 7 angles
900 deg. angles Total, deg. each
7 vertices, 4 diagonals from single vertex
8 sided figure, 8 angles
1080 deg. angles Total, 135 deg. each
8 vertices, 5 diagonals from single vertex

9. Angles and Diagonals in Regular Polygons
Example: Octagon
S=8
D=(8-3)=5
T=(8-3)+1=6
6 (T)x 180= 1080 degrees total
1080 degrees/ 8 angles= 135 degrees per angle
Side (S) = X
Diagonal (D) = (X-3)
Triangle (T) = {(X-3)+1} (X-2)
135 degree angle
180 degree (straight line)-135 degrees (interior angle)= 45 degrees (exterior angle)

10. 1260 deg. angles Total, 140 deg. each
Nonagon
Decagon
9 sided figure, 9 angles
1260 deg. angles Total, 140 deg. each
9 vertices, 6 diagonals from single vertex
10 sided figure, 10 angles
1440 deg. angles Total, 144 deg. each
10 vertices, 7 diagonals from single vertex

11. Sources http://www.mathleague.com/help/geometry/polygons.htm
Grandfather Tang’s Story (A Tale With Tangrams) by Ann Tompert