Classifications of Polygons
You might be aware of certain names of special polygons, such as pentagon, hexagon, and octagon. These terms classify a polygon by the number of sides. In fact, the common names of polygons with 3 to 10 sides are:
# sides 
name 
examples 
3 
triangle 

4 
quadrilateral 

5 
pentagon 

6 
hexagon 

7 
heptagon 

8 
octagon 

9 
nonagon 

10 
decagon 
You may be surprised that an object like this is called a pentagon:  
We are accustomed to seeing pentagons that look like this: 
Both these figures are polygons with 5 sides according to our definition. What is peculiar about the first figure is it "caves in" at the top. Such a polygon is called concave. In fact, a definition of "concave" is this:
DEFINITION: A polygon is concave if there are two points somewhere inside it for which a segment with these as its endpoints cuts at least 2 of the sides of the polygon.
For example,

is concave, because the segment with points A and B as its endpoints cuts two sides:

A polygon that is not concave is called convex. Some important theorems that apply only to convex polygons will be stated in the next lesson.