3 5 angles of a polygon
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3-5 Angles of a Polygon
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What is a polygon?• The word polygon means “many
angles.”• Polygons are formed by
coplanar segments (sides) such that:– Each segment intersects exactly
two other segments, one at each endpoint.
– No two segments with a common endpoint are collinear.
(These 2 are NOT polygons, why do you think this is?)
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Convex Polygon and Parts of a 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.
Nonconvex polygons are often referred to as concave polygons. When we refer to a polygon, we will mean a convex polygon.
Parts of a polygon include the sides, angles, exterior angles, vertices, and diagonals.
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Sum of the measures of the angles in a polygon:
4 sides, 2 trianglesAngle sum = 2(180)
5 sides, 3 trianglesAngle sum = 3(180)
6 sides, 4 trianglesAngle sum = 4(180)
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Theorems
Theorem 3-13
The sum of the measures of the angles of a convex polygon with n sides is (n – 2)180.
Theorem 3-14
The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
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Regular Polygons• Polygons can be
equiangular or equilateral.
• If a polygon is both equiangular and equilateral, then it is called a regular polygon.
• Examples
120° 120°120°120°
120°120°Equiangular
Equilateral
120° 120°120°
120°
120°120°
Regular Hexagon
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