1 polygons keystone geometry. 2 these figures are not polygonsthese figures are polygons...
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PolygonsKeystone Geometry
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These figures are not polygons These figures are polygons
Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.
Polygons
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Classifications of a PolygonConvex: No line containing a side of the polygon contains a point
in its interior
Concave:
A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
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Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length
Irregular: Two sides (or two interior angles) are not congruent.
Classifications of a Polygon
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Polygon NamesClassified by the number of sides
3 sides Triangle4 sides5 sides6 sides7 sides8 sides
NonagonOctagonHeptagonHexagonPentagonQuadrilateral
10 sides9 sides
12 sides
DecagonDodecagon
n sides n-gon
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Convex Polygon Formulas…..Diagonals of a Polygon:
For a convex polygon with n sides:
A segment connecting nonconsecutive vertices of a polygon
• The more sides a polygon has, the more diagonals it will have. • A square has 2 diagonals.• A pentagon has 5 diagonals.• A hexagon has 9 diagonals………
Examples
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Diagonals in a square, n = 4
Diagonals in an octagon, n = 8
** What about a triangle?A triangle does not have ANY diagonals.
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Polygon Angle FormulasFinding the INTERIOR angles in a convex polygon with n sides:
The sum of the interior angles is
The measure of one interior angle is
The sum of the exterior angles is
The measure of one exterior angle is
Finding the EXTERIOR angles in a convex polygon with n sides:
Solving for the Angles
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Polygon Triangle Quadrilateral Pentagon Hexagon
Interior Angle Sum
180 360 540 720
Each Interior Angle
60 90 108 120
Exterior Angle Sum
360 360 360 360
Each Exterior Angle
120 90 72 60
Solving for the Angles
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Polygon Heptagon Octagon Nonagon Decagon
Interior Angle Sum
Each Interior Angle
Exterior Angle Sum
Each Exterior Angle
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Examples…..1. Sum of the measures of the interior angles of a 11-gon is
(n – 2)180° (11 – 2)180 ° 1620
2. The measure of an exterior angle of a regular octagon is
3. The number of sides of regular polygon with exterior angle 72 ° is
4. The measure of an interior angle of a regular polygon with 30 sides