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Section 1.6 Classifying Polygons
Geometry
What is a polygon?
A polygon is:
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- a closed figure,
- formed by three or more line segments called sides, where,
- each side intersects only two other sides, each at their endpoints, called a
vertex (singular) or vertices (multiple).
Q
This polygon is named by listing all vertices in
consecutive order. For example, it could be
called QRSWT. What's another?
R
T
Sides
Sides
andSSare
areboth
both
RRand
vertices
vertices
W
S
Convex vs. Concave Polygon
...What's the difference?
Convex Polygons: A polygon in which no line containing a side of the
polygon contains a point in the interior of the polygon.
B
A
C
D
Convex vs. Concave Polygon
...What's the difference?
Concave Polygons: (Opposite of Convex) A polygon that does contain at
least one line that contains a side of a polygon that
passes through the interior of the polygon.
B
A
C
E
D
Polygon ABCDE is concave because BC and DC contains points on the interior of the polygon.
Polygon Names: A polygon is named by the number of sides.
Number of Sides
Type of Polygon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
n
n - gon
...where n is the number of sides on a given polygon.
Match the term to the appropriate shape!
Equilateral (all sides congruent)
Equiangular (all interior angles congruent)
Regular (equilateral and equiangular)
Pentagon
Convex
Polygon
Quadrilateral
Concave
"Closed" Figure
Octagon
Nonagon
Classify the given polygons.
Example 1
Two sides of a regular octagon are represented by the expressions, (4x - 2) inches
and (3x + 4) inches. What is the length of one side of the octagon? What is the
perimeter?
Example 2
The figure below is equilateral. What is length of one side?
x2 + 5x - 10
x2 - 3x + 14
*
Learning Targets: