# Introduction to Polygons

You may want to review:

*polygon*is a closed figure in a plane made by joining line segments, where each line segment intersects exactly two others.

Note: Strictly speaking, a polygon does
*not* include its interior
(the space inside the polygon).

not a polygon

not a polygon

not a polygon

Polygons are usually classified according to how many sides they have:

*triangle*is a polygon with $\,3\,$ sides.

*quadrilateral*is a polygon with $\,4\,$ sides.

*pentagon*is a polygon with $\,5\,$ sides.

*hexagon*is a polygon with $\,6\,$ sides.

*heptagon*is a polygon with $\,7\,$ sides.

*octagon*is a polygon with $\,8\,$ sides.

*nonagon*is a polygon with $\,9\,$ sides.

*decagon*is a polygon with $\,10\,$ sides.

More generally, a polygon with $\,n\,$ sides can be called an $\,n\,$-gon.

For example, a polygon with $\,27\,$ sides can be called a $\,27$-gon.

The *vertices* of a polygon
are the points where its sides intersect.
The singular form of *vertices*
is *vertex*.

## Naming Polygons

When naming polygons, the vertices must be listed in consecutive order. For example, the polygon above could be named:

- polygon $\,ABCD\,$ (start with $\,A\,,$ move clockwise)
- polygon $\,ADCB\,$ (start with $\,A\,,$ move counter-clockwise)
- polygon $\,BCDA\,$ (start with $\,B\,,$ move clockwise)
- polygon $\,BADC\,$ (start with $\,B\,,$ move counter-clockwise)
- polygon $\,CDAB\,$ (start with $\,C\,,$ move clockwise)
- polygon $\,CBAD\,$ (start with $\,C\,,$ move counter-clockwise)
- polygon $\,DABC\,$ (start with $\,D\,,$ move clockwise)
- polygon $\,DCBA\,$ (start with $\,D\,,$ move counter-clockwise)

More generally, when naming an $\,n$-gon, there are $\,n\,$ choices for listing the first vertex. Then, there are $\,2\,$ choices for the next vertex (moving clockwise or counterclockwise). The remaining vertices are then completely determined. Thus, there are $\,2n\,$ choices for the polygon name.

*regular polygon*is a polygon whose sides all have the same length, and whose angles are all the same.

(a square)

A *rectangle* is
a quadrilateral whose angles are
all right angles.

A *square* is a
rectangle with all sides of equal length.

Note: Every square is a rectangle. However, not every rectangle is a square. That is, there exist rectangles that are not squares.

Each of these is a rectangle,
but *not* a square.

For fun, jump up to
WolframAlpha and type in (say)
‘triangle’ or ‘quadrilateral’.
You'll get *loads* of information!