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Understanding Polygons: Definitions, Types, and Classifications

This comprehensive guide provides an overview of polygons, defining them as enclosed figures with at least three sides that only intersect at their endpoints. It explores the components of polygons, including vertices, sides, angles, and diagonals. The distinction between convex and concave polygons is explained, along with the criteria for classifying polygons based on the number of sides. Various types such as regular and irregular polygons are discussed, highlighting examples like triangles, quadrilaterals, and dodecagons.

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Understanding Polygons: Definitions, Types, and Classifications

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  1. Polygons---Terms Geometry (Holt 6-1) K. Santos

  2. Polygon Polygon—enclosed figure --has at least 3 sides (segments) --sides only intersect at their endpoints --no adjacent sides are collinear --poly (many) gon (sides)

  3. Examples on Non-polygons

  4. Parts of a Polygon Angles A B <A, <B, <C, <D, <E, <F Vertices (1—Vertex)--corners A, B, C, D, E, F F C Sides (segments) ,, , , , Specific Name: (must list clockwise or counterclockwise) ABCDEF E D DEFABC EDCBAF

  5. Diagonals A segment that connects two nonconsecutive vertices. A B Diagonals: F C E D

  6. Convex vs Concave Extend the sides of the polygon to figure out if a figure is convex or concave. If all the extensions stay outside of the polygon then it is convex. If any of the extensions go into the polygon then it is concave. concave

  7. Equiangular/Equilateral/Regular Equiangular—all equal/congruent angles Equilateral—all equal/congruent sides Regular polygon—both equiangular and equilateral

  8. Regular vs irregular polygon Regular Polygons Irregular Polygons

  9. Classifying polygon based on number of Sides Number of Sides Name of polygon 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 septagon/heptagon 8 octagon 9 nonagon 10 decagon 11 undecagon 12 dodecagon 13 13-gon n n-gon

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