Download - Polygons
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POLYGONS
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polygon not a polygon
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• A polygon is a plane figure.• A polygon is a closed region.• A polygon is formed by three or more
segments as its sides.• Each side of a polygon intersects only
one segment at each of its endpoints.• poli + gonus “many angled”
What is a polygon?
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Polygon or Not a Polygon?
Polygon
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Polygon or Not a Polygon?
Not Polygonbecause sides are not segments.
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Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting not just at the endpoints.
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Polygon or Not a Polygon?
Polygon
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Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting not just at the endpoints.
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Polygon or Not a Polygon?
Polygon
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Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting more than one other side at its endpoint.
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Regions in a Polygon
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Parts of a Polygon
•sides▫consecutive sides
included angle▫nonconsecutive sides
•interior angles / vertex angles▫consecutive angles
included side▫nonconsecutive angles
•exterior angles•diagonals
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ALL POLYGONS
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ALL POLYGONS???
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ALL POLYGONS!
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How can these polygons be divided into two groups?
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Convex PolygonsConcave Polygons
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Polygon Convexity
A polygonal region is convex if any segment joining any two points of the polygon is part of the interior region.
If a polygon is not convex, then its is concave.
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Convex or Concave?
Convex
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Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
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Convex or Concave?
Convex
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Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
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Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
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Convex or Concave?
Convex
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Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
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Polygons are named by writing their consecutive vertices in order, such as ABCD or CDAB for the polygon above.
We cannot name the polygon as DBAC.
NAMING POLYGONS
BA
CD
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Connecting to Prior Knowledge•Think of words
beginning with the prefixes tri-, quad-, pent-, and oct-.
•Examples: triathlon, quadriplegic, pentameter, and octopus.
•Meanings? (words and prefixes)
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Polygons can be named by their number of sides.
Number of Sides Name of Polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon
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EQUIANGULAR POLYGONEQUILATERAL POLYGONREGULAR POLYGON
Concept Emphasis
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EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR
EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR
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