Download 6.1: Polygons polygon: closed plane figure consisting of 3 or more

January 23, 2012
6.1: Polygons
polygon: closed plane figure consisting of 3 or more
segments (sides) with no 2 sides with a common
endpoint are collinear and each side intersects
exactly 2 other sides, one at each endpoint.
Which are polygons? Why/why not?
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convex / concave:
convex: if no line containing a side lies in the interior
concave: if a line containing a side lies in the interior
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regular polygons: equilateral and equiangular
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Names:
# of sides name
3
4
5
6
7
8
9
10
11
12
15
n
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Diagonal: segment joining 2 nonconsecutive sides
A
B
E
D
C
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Polygon # of sides
triangle
quadrilateral
pentagon
hexagon
# of triangles
Sum of interior
angles
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1. Find the sum of the measures of the interior angles of
a convex heptagon.
2. Find the measure of each interior angle of a regular 16-gon.
3. Find the measure of each interior angle of pentagon
ABCDE.
C
32x
B
32x
18x
D
18x
35x
A
E
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Is the quadrilateral regular?
x
80
x-20
x
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Find x.
x
55
80
70
x
x
2x
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Polygon Exterior Angle Sum Theorem:
The sum of the measures of the exterior angles, one at
each vertex, of a convex polygon is 360o
Proof:
Sext = Sall int/ext - Sint
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1. Find the measure of each exterior angle of a regular 20-gon.
2. Find x.
16x
33x
10x
28x
18x
15x