audio read-through Introduction to Polygons

You may want to review:

DEFINITION polygon
A 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).

a polygon A polygon
not closed; not a polygon Not closed;
not a polygon
not made of line segments; not a polygon Not made of line segments;
not a polygon
line segment intersects more than two others; not a polygon Line segment intersects more than two others;
not a polygon

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

DEFINITIONS names of polygons with various numbers of sides
a triangle A triangle is a polygon with $\,3\,$ sides.
a quadrilateral A quadrilateral is a polygon with $\,4\,$ sides.
a pentagon A pentagon is a polygon with $\,5\,$ sides.
a quadrilateral A hexagon is a polygon with $\,6\,$ sides.
a heptagon A heptagon is a polygon with $\,7\,$ sides.
an octagon An octagon is a polygon with $\,8\,$ sides.
a nonagon A nonagon is a polygon with $\,9\,$ sides.
a decagon A 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.

DEFINITION vertex of a polygon; vertices

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

vertex; vertices

Naming Polygons

naming polygons

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

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.

DEFINITION regular polygon
A regular polygon is a polygon whose sides all have the same length, and whose angles are all the same.
a regular triangle a regular triangle
a regular quadrilateral (a square) a regular quadrilateral
(a square)
a regular pentagon a regular pentagon
a regular hexagon a regular hexagon
a regular heptagon a regular heptagon
a regular octagon a regular octagon
a regular nonagon a regular nonagon
a regular decagon a regular decagon
DEFINITIONS rectangle, 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.

a rectangle, but not a square a rectangle, but not a square

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!

Concept Practice