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.