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When points or
lines are arranged in some
formation, rarely
does it result in a recognizable geometric figure. Well-known shapes like
squares and triangles are actually only subsets of larger groups of
geometric figures and other collections of points in
space.

One of the easiest and most common collections of points in space is a
curve. A curve can be any continuous arrangement of points, straight or
curved, in space. A curve can be defined as the trace of the motion of a point
in space. So a curve is like a path through space by which a point could
travel. For our purposes, we'll only consider curves that lie in a
plane. A curve is continuous,
meaning that
there aren't any gaps or holes in the curve; any point on a curve can be reached
from another point on the curve without leaving the curve. A dotted line, for
example, is not a curve. Here are some examples of curves below.

A curve whose starting point is also its endpoint is called a closed curve.
The reason for this is that such a curve encloses a region in the plane. A
simple closed curve is an even more specific kind of curve: one that is
closed, and doesn't intersect itself. The region enclosed by a simple
closed curve is not divided by any part of the curve. Closed curves sometimes
intersect themselves, but not simple closed curves. Below are some closed
curves and simple closed curves.

Polygons

A polygon is one type of simple closed curve. A polygon is the union of
three or more line segments whose
endpoints
meet. The segments are called the sides of the polygon. The points at
which the segments meet (always the endpoints of the segments) are called
vertices. Segments that share a vertex are called adjacent sides.
Vertices next to each other are called consecutive vertices. A segment
whose endpoints are nonadjacent vertices is called a diagonal.
See the
picture below.

A polygon is named for its vertices, but the vertices must be listed in order.
It doesn't matter which direction the order goes, as long as consecutive
vertices are next to each other in the name. The first and last letters in the
name, of course, are consecutive vertices, but won't be listed next to each
other. For example, the polygon above could be called BCDEFA, or EDCBAF, or
some other name incorporating the six vertices in order.

Classifying Polygons

Polygons can be classified and named based on how many sides they have. In the
table below are these names.