Polygons 100830211438-phpapp01

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Polygons 100830211438-phpapp01

  1. 1. polygon not a polygon
  2. 2. What is 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”
  3. 3. Polygon or Not a Polygon?
  4. 4. Polygon or Not a Polygon? Polygon
  5. 5. Polygon or Not a Polygon?
  6. 6. Polygon or Not a Polygon? Not Polygon because sides are not segments.
  7. 7. Polygon or Not a Polygon?
  8. 8. Polygon or Not a Polygon? Not Polygon because sides are intersecting not just at the endpoints.
  9. 9. Polygon or Not a Polygon?
  10. 10. Polygon or Not a Polygon? Polygon
  11. 11. Polygon or Not a Polygon?
  12. 12. Polygon or Not a Polygon? Not Polygon because sides are intersecting not just at the endpoints.
  13. 13. Polygon or Not a Polygon?
  14. 14. Polygon or Not a Polygon? Polygon
  15. 15. Polygon or Not a Polygon?
  16. 16. Polygon or Not a Polygon? Not Polygon because sides are intersecting more than one other side at its endpoint.
  17. 17. Regions in a Polygon
  18. 18. Parts of a Polygon• sides ▫ consecutive sides  included angle ▫ nonconsecutive sides• interior angles / vertex angles ▫ consecutive angles  included side ▫ nonconsecutive angles• exterior angles
  19. 19. 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.
  20. 20. ALL POLYGONS
  21. 21. ALL POLYGONS???
  22. 22. ALL POLYGONS!
  23. 23. How can these polygons be divided into two groups?
  24. 24. Convex Polygons Concave Polygons
  25. 25. Polygon ConvexityA 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.
  26. 26. Convex or Concave? Convex
  27. 27. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.
  28. 28. Convex or Concave? Convex
  29. 29. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.
  30. 30. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.
  31. 31. Convex or Concave? Convex
  32. 32. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.
  33. 33. A B D C 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.
  34. 34. • Think of words beginning with the prefixes tri- , quad-, pent-, and oct-.• Examples: triathlon, quadriplegic, pen tameter, and octopus.• Meanings? (words and prefixes)
  35. 35. 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
  36. 36.  EQUIANGULAR POLYGON EQUILATERAL POLYGON REGULAR POLYGON
  37. 37. EQUILATERAL but not EQUILATERAL and EQUIANGULAR EQUIANGULAR ┌ ┌ ┌ ┌ EQUILATERAL and EQUIANGULAR but not EQUIANGULAR EQUILATERAL ┌ ┌ ┌ ┌
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