Introduction to Polygons

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INTRODUCTION TO POLYGONS

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Here are additional illustrations of polygons: http://www.mathleague.com/help/geometry/polygons.htm

DEFINITION: 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	not closed; not a polygon	not made of line segments; 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:

A *triangle* is a polygon with 3 sides.		A *heptagon* is a polygon with 7 sides.
A *quadrilateral* is a polygon with 4 sides.		An *octagon* is a polygon with 8 sides.
A *pentagon* is a polygon with 5 sides.		A *nonagon* is a polygon with 9 sides.
A *hexagon* is a polygon with 6 sides.		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: The vertices of a polygon are the points where its sides intersect.
The singular form of vertices is vertex.
vertex; vertices

NAMING POLYGONS:
When naming polygons, the vertices must be listed in consecutive order.
For example, the polygon at right below 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.

DEFINITION: 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 quadrilateral (a square)	a regular pentagon	a regular hexagon


a regular heptagon	a regular octagon	a regular nonagon	a regular decagon

DEFINITION: A rectangle is a quadrilateral whose angles are all right angles.

DEFINITION: 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

On this exercise, you will not key in your answers.
However, you can check to see if your answer is correct.