Transcript geom lesson 15- 2009-10

Polygons
A Polygon is a closed plane figure
formed by 3 or more segments
Each segment intersects exactly 2 other
0011 0010 1010
1101 0001 0100
1011 at their endpoints.
segments
only
No 2 segments with a common endpoint
are collinear
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Sides
• The segments that form a
polygon are called its
sides.
• In a polygon, no 2
segments with a common
endpoint are collinear
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Vertex of a Polygon
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• The vertex of a polygon is the intersection
of 2 of its sides.
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EQUIANGULAR POLYGON
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• An equiangular polygon is a polygon in
which all angles are congruent
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Equilateral Polygon
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• An equilateral polygon is a polygon in
which all sides are congruent.
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REGULAR POLYGON
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• If a polygon is both equiangular and
equilateral, then it is called regular.
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Irregular Polygon
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• If a polygon is not equiangular and
equilateral, then it is an irregular polygon
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Polygons named by number of sides
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11 sided polygon - hendecagon
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Diagonal of a polygon
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• A diagonal of a polygon is a segment that
connects 2 nonconsecutive vertices.
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Convex polygon
• In a convex polygon, every diagonal lies inside it
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Concave polygon
• In a concave polygon, at least 1 diagonal can be
drawn
so
that
part
of
it
contains
points
in
the
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exterior of the polygon
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Congruent polygons
• If 2 polygons have the same size and
they
0011 0010shape,
1010 1101
0001 are
0100 congruent
1011
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Interior and Exterior angles of polygons
• At each vertex, there are 2 special angles.
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•0011An
interior angle is an angle fprmed by 2 sides of a
polygon with a common vertex
• An exterior angles is an angle formed by 1 side of a
polygon and the extension of an adjacent side
E
I
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Formula for sum of interior
angles of a polygon
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• n is the number of sides
1
sum of interior angles = (n-2)
2
o
180
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Formula for interior angles
measure of a regular polygon
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• n is the number of sides
• Each interior angle =
n  2g
180 1
b
n
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Formula for exterior angle
measure of a regular polygon
• n is the number of sides
0011 0010 1010 1101 0001 0100 1011
360
n
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Center of a regular polygon
• Center is the point that is
equidistant from each of
the polygon's vertices
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Central angle of a regular
polygon
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• Central angle has its vertex at the center of
the polygon and its sides pass through
consecutive vertices
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Formula for central angle
measure of a regular polygon
0011 0010 1010 1101 0001 0100 1011
• n is the number of sides
360
n
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4
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