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Unit 2 Polygons In The Plane

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These figures are not polygonsThese 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 Polygon Convex: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 Names 3 sides Triangle 4 sides 5 sides 6 sides 7 sides 8 sides Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral 10 sides 9 sides 12 sides Decagon Dodecagon n sides n-gon

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Convex Polygon Formulas….. Diagonals of a Polygon: For a convex polygon with n sides: The sum of the interior angles is A segment connecting nonconsecutive vertices of a polygon The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is

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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 ° 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

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The End!

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