Polygons

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Polygons
Objectives To identify and name polygons To find
the sum of the measures of interior and exterior
angles of convex and regular polygons To solve
problems involving angle measures of polygons
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Polygons
Polygon
A polygon is a closed figure formed by a finite
number of coplanar segments such that the sides
that have a common endpoint are noncollinear and
each side intersects exactly two other sides, but
only at their endpoints
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Polygons
Examples are
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Polygons
Convex Polygon
A convex polygon is a polygon such that no line
containing a side of the polygon contains a point
in the interior of the polygon. Examples are
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Polygons
Concave Polygon
A concave polygon is a polygon such that the
lines containing a side of the polygon contains a
point in the interior of the polygon. Examples
are
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Polygons
A n-gon is a polygon with n sides
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Polygons
Regular Polygon
A regular polygon is a convex polygon with all
sides and angles congruent
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Polygons
Theorems
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Polygons
Interior Angle Sum Theorem
If a convex polygon has n sides and S is the sum
of the measures of its interior angles, then S
180(n 2)
Find the sum of a convex polygon that has 3 sides
Find the measure of each interior angle of a
regular hexagon
S 180(3 2) S 180
First find the sum of all of the angles in the
hexagon
S 180(6 2) S 720
Then to find the measure of each interior angle,
divide the sum of the angles by the number of
angles in the hexagon
720/6 or 120
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Polygons
Exterior Angle Sum Theorem
If a polygon is convex, then the sum of the
measures of the exterior angles, one at each
vertex, is 360
Use the Exterior Angle Sum Theorem to find the
measure of an interior angle and an exterior
angle of a regular polygon
A regular polygon has 5 congruent interior
angles. So the measure of each exterior angle is
360/5 or 72
Because each exterior angle is supplementary to
each interior angle the measure of each interior
angle is
180 2 or 108
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Polygons
Homework!
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Polygons
pp. 519-520 Problem numbers 22-56 even