This document defines and describes different types of polygons. A polygon is a flat shape formed by three or more straight line segments that are connected and do not intersect except at endpoints. Polygons are named based on the number of sides, such as triangles having 3 sides, quadrilaterals having 4 sides, and pentagons having 5 sides. Polygons can be either convex, where the interior angles add up to more than 180 degrees, or concave, where at least one interior angle is greater than 180 degrees. Special types of polygons include equilateral, equiangular, and regular polygons which have consistent side lengths, interior angles, or both.

1. 3.5 Polygons

2. A polygon:
Formed by 3 or more segments
(sides), no two sides with common
endpoints are collinear
Each side intersects exactly 2 other
sides, one at each end point
Endpoints are called a Vertex
(vertices)

3. Naming Polygons
Name by vertices
Ex: polygon ABCDEFG
Name by sides

4. # of Sides Type
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
n n-gon

5. Convex or Concave?
“Concave”
Looks like it is “caving” in
“Convex”
The other kind (close to a
circle)

6. Convex
pentagon Concave
pentagon
Concave
octagon
Convex
heptagon

7. Special Polygons
Equilateral
All sides the same
Equiangular
All angles the same
Regular
All sides and angles the same

8. Regular none of the above Regular
Regular Not a polygonequiangluar

9. Diagonals:
Connect two
nonconsecutive
vertices
Polygon PQRST
has two diagonals
from Q, QT and
QS
P
Q
R
S
T
P
Q
R
S
T