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Geometry
Section 6.1
Polygons
The word polygon means many
sides.
In simple terms, a polygon is a
many-sided closed figure.
Formally, a polygon is a figure formed from
three or more line segments such that each
segment intersects exactly two other segments,
one at each endpoint, and no two segments
with a common endpoint are collinear.
The segments are called the_____
sides of
the polygon and the common
vertices of
endpoints are called the _______
the polygon.
When naming a polygon, you must
list the vertices in order either
clockwise or counterclockwise.
The polygon at the right could be
named _______
BAFEDC
ABCDEF or _______
A diagonal of a polygon is a
segment joining two nonadjacent
vertices.
A polygon is equilateral iff
all its sides are congruent.
A polygon is equiangular iff
all its angles are congruent.
A polygon that is both equilateral
and equiangular is called a
_______
regular polygon.
The center of a regular polygon is
the point which is equidistant from
each of the vertices.
A central angle of a polygon is an
angle whose vertex is the center
and whose sides are radii.
A polygon is convex iff the line
containing a side does not contain
a point in the interior.
A polygon that is not convex is
concave.
Polygons are classified according to
the number of its sides.
triangle
3 - ____________
5 - ____________
pentagon
7 - ____________
heptagon
nonagon
9 - ____________
dodecagon
12 - ___________
4 - ____________
quadrilateral
hexagon
6 - ____________
octagon
8 - ____________
decagon
10 - ___________
n - ___________
n - gon
Example: How many diagonals can
be drawn from one vertex in a
hexagon?
diagonals from 1 vertex  # of vertices - 3
Example: How many total
diagonals can be drawn in a
hexagon? a heptagon?
3
3
2
1
Example: What would you call a
regular quadrilateral?
square
Example: Draw a nonconvex
octagon.
Example: What is the measure of
each central angle in a regular
pentagon? dodecagon?
360
360  72
5
12
 30