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Polygons
Lesson 3-4: Polygons
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Polygons
Definition: A closed figure formed by a finite number of coplanar
segments so that each segment intersects exactly two
others, but only at their endpoints.
These figures are not polygons
Lesson 3-4: Polygons
These figures are polygons
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Classifications of a Polygon
Convex: No line containing a side of the polygon contains a point
in its interior
Concave:
A polygon for which there is a line
containing a side of the polygon and
a point in the interior of the polygon.
Lesson 3-4: Polygons
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Classifications of a Polygon
Regular: A convex polygon in which all interior angles have the
same measure and all sides are the same length
Irregular: Two sides (or two interior angles) are not congruent.
Lesson 3-4: Polygons
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Polygon Names
3 sides
Triangle
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
9 sides
Nonagon
10 sides
Decagon
12 sides
n sides
Dodecagon
n-gon
Lesson 3-4: Polygons
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Convex Polygon Formulas…..
Diagonals of a Polygon: A segment connecting nonconsecutive
vertices of a polygon
 n  2  180
n
For a convex polygon with n sides:
The sum of the interior angles is
 n  2 180
The measure of one interior angle is
360
The sum of the exterior angles is
The measure of one exterior angle is
360
n
Lesson 3-4: Polygons
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Examples…..
1. Sum of the measures of the interior angles of a 11-gon is
(n – 2)180°  (11 – 2)180 °  1620
2. The measure of an exterior angle of a regular octagon is
360 360

 45
n
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3. The number of sides of regular polygon with exterior angle 72 ° is
exterior angle 
360
360
360
n
n
5
n
exterior angle
72
4. The measure of an interior angle of a regular polygon with 30 sides
 n2 180  (302)180  28180  168
n
30
30
5. The number of sides of regular polygon with interior angle 172 ° is
 n2 180  172  180n  360  172n
n
8n  360  n  45
Lesson 3-4: Polygons
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