Geometry Ch.6
6.1 Classify Polygons
Identifying Polygons
In geometry, a figure that lies in a plane is
called a plane figure. A polygon is a
closed plane figure with the following
properties.
It is formed by three or more line segments
called sides.
Each side intersects exactly two sides, one
at each endpoint, so that no two sides
with a common endpoint are collinear.
Each endpoint of a side is a vertex of the
polygon. The plural of vertex is vertices. A
polygon can be named by listing the vertices
in consecutive order. The polygon shown
here has six vertices. It is a hexagon.
A polygon is convex if no line that
contains a side of the polygon contains
a point in the interior of the polygon. A
polygon that is not convex is called
nonconvex or concave.
Convex
Concave
Classifying Polygons: A polygon is
named by the number of its sides
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
8
octagon
9
nonagon
10
decagon
12
dodecagon
n
n-gon
The term n-gon, where n is the number of a polygon’s
sides, can also be used to name a polygon. For example,
a polygon with 14 sides is a 14-gon.
In an equilateral polygon, all sides are
congruent.
In an equiangular polygon, all angles in the
interior of the polygon are congruent.
A regular polygon is a convex polygon that is
both equilateral and
equiangular.
Regular polygons
are shown to the
right.
Ex.1
Practice—any volunteers to sketch
an example of a convex hexagon
and a concave hexagon?
Ex.2: Extra practice: Using properties, tell
whether the statement is always,
sometimes, or never true.
A triangle is convex
A decagon is regular
A regular polygon is equiangular
A circle is a polygon
A polygon is a plane figure
A concave polygon is regular
Ex. 3.
Let x be the length in inches. If a figure is a
regular decagon, and the length of one side is
2x + 8 and the length of another side is 4x +
4, find the length of each side of this regular
decagon.
Ex. 3.
Let x be the length in inches. If a figure is a
regular decagon, and the length of one side is
2x + 8 and the length of another side is 4x +
4, find the length of each side of this regular
decagon.
2x + 8 = 4x + 4
2 x =4x – 4
-2 x = – 4
x=2
2(2) + 8=12
The length of each side is 12 inches
Theorem 6.1
Interior Angles of a Quadrilateral
The measure of the interior
angles of a quadrilateral is 360
degrees.
Websites used in preparation for this PPT:
www.seal-pa.org
www.mathleague.com
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/Image434
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