Download Polygons

Polygons
Define:
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Concave Polygon:
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Convex Polygon:
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Diagonal:
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Perimeter:
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Polygon:
 Regular Polygon:
Polygon Characteristics:
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Closed flat geometric figures
No side is curved
Nonconsecutive sides don’t intersect
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At least 3 sides
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Consecutive sides intersect only at endpoints
Consecutive sides must be noncollinear.
Each segment of polygon is called side and
each endpoint of side is called vertex.
The number of sides is always equal to the
number of vertices.
Each vertex must belong to exactly 2 sides
Examples: Polygon?
Determine which of the following are polygons and which are not. If they are not, indicate the reason why.
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5.
Naming Polygons:
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Start at any vertex and precede either clockwise or counterclockwise.
Use the letters of the polygon’s vertices.
Examples: Naming Polygons
Identify all possible names for the following polygons.
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2.
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Rev B
Polygons
Classifying Polygons:
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Name each polygon by the # of its sides.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
# of Sides
# of ∆
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Sum of Angle Measures
Identify if convex/concave and regular/irregular.
Polygon
Octagon
Nonagon
Decagon
Dodecagon
N-gon
# of Sides
# of ∆
Sum of Angle Measures
Examples: Classify Polygons
Classify each polygon based on # of sides, convex/concave and regular/irregular.
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2.
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Examples: Determining Interior Angles
1. Find the measure of each interior angle.
2. Find the measure of the missing angle.
Polygon Formulas:
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Sum Si of measures of angles of polygon with n sides: Si = (n-2)180
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If 1 exterior angle is taken at each vertex, sum Se of measures of exterior angles of polygon: Se = 360
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Number d of diagonals that can b drawn in polygon of n sides: d = n(n-3)/2
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Measure E of each exterior angle of equiangular polygon of n sides: E = 360/n
Examples: Using Polygon Formulas
1. Find the sum of the interior angles of a
dodecagon.
2. Find the sum of the exterior angles of a
dodecagon.
3. Find the number of diagonals that can be
drawn in a dodecagon.
4. Find the measures of an exterior angle and an
interior angle of convex regular octagon.
5. The measure of an interior angle of a regular polygon is 108. Find the number of sides in the polygon.
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Rev B