Post on 25-Dec-2014
description
POLYGONS
polygon not a polygon
• 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?
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are not segments.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting not just at the endpoints.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting not just at the endpoints.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting more than one other side at its endpoint.
Regions in a Polygon
Parts of a Polygon
•sides▫consecutive sides
included angle▫nonconsecutive sides
•interior angles / vertex angles▫consecutive angles
included side▫nonconsecutive angles
•exterior angles
Parts of a Polygon
•Diagonals▫A diagonal of a polygon is any segment
that joins two nonconsecutive vertices. Figure shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon.
ALL POLYGONS
ALL POLYGONS???
ALL POLYGONS!
How can these polygons be divided into two groups?
Convex PolygonsConcave Polygons
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.
Convex or Concave?
Convex
Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
Convex or Concave?
Convex
Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
Convex or Concave?
Convex
Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
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
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)
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
EQUIANGULAR POLYGONEQUILATERAL POLYGONREGULAR POLYGON
Concept Emphasis
EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR
EQUIANGULAR but not EQUILATERAL
EQUILATERAL and EQUIANGULAR
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