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Polygons

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Polygons

  1. 1. POLYGONS<br />
  2. 2. polygon<br />not a polygon<br />
  3. 3. A polygon is a plane figure.<br />A polygon is a closed region.<br />A polygon is formed by three or more segments as its sides.<br />Each side of a polygon intersects only one segment at each of its endpoints.<br />poli + gonus “many angled”<br />What is a polygon?<br />
  4. 4. Polygon or Not a Polygon?<br />Polygon<br />
  5. 5. Polygon or Not a Polygon?<br />Not Polygon<br />because sides are not segments.<br />
  6. 6. Polygon or Not a Polygon?<br />Not Polygon<br />because sides are intersecting not just at the endpoints.<br />
  7. 7. Polygon or Not a Polygon?<br />Polygon<br />
  8. 8. Polygon or Not a Polygon?<br />Not Polygon<br />because sides are intersecting not just at the endpoints.<br />
  9. 9. Polygon or Not a Polygon?<br />Polygon<br />
  10. 10. Polygon or Not a Polygon?<br />Not Polygon<br />because sides are intersecting more than one other side at its endpoint.<br />
  11. 11. Regions in a Polygon<br />
  12. 12. Parts of a Polygon<br />sides<br />consecutive sides<br />included angle<br />nonconsecutive sides<br />interior angles / vertex angles<br />consecutive angles<br />included side<br />nonconsecutive angles<br />exterior angles<br />diagonals<br />
  13. 13. ALL POLYGONS<br />
  14. 14. ALL POLYGONS???<br />
  15. 15. ALL POLYGONS!<br />
  16. 16. How can these polygons be divided into two groups?<br />
  17. 17. Convex Polygons<br />Concave Polygons<br />
  18. 18. Polygon Convexity<br />A polygonal region is convex if any segment joining any two points of the polygon is part of the interior region.<br />If a polygon is not convex, then its is concave.<br />
  19. 19. Convex or Concave?<br />Convex<br />
  20. 20. Convex or Concave?<br />Concave<br />because a segment connecting points on the polygon that will lie in the exterior can be drawn.<br />
  21. 21. Convex or Concave?<br />Convex<br />
  22. 22. Convex or Concave?<br />Concave<br />because a segment connecting points on the polygon that will lie in the exterior can be drawn.<br />
  23. 23. Convex or Concave?<br />Concave<br />because a segment connecting points on the polygon that will lie in the exterior can be drawn.<br />
  24. 24. Convex or Concave?<br />Convex<br />
  25. 25. Convex or Concave?<br />Concave<br />because a segment connecting points on the polygon that will lie in the exterior can be drawn.<br />
  26. 26. Naming Polygons<br />B<br />A<br />D<br />C<br />Polygons are named by writing their consecutive vertices in order, such as ABCD or CDAB for the polygon above.<br />We cannot name the polygon as DBAC.<br />
  27. 27. Connecting to Prior Knowledge<br />Think of words beginning with the prefixes tri-, quad-, pent-, and oct-.<br />Examples: triathlon, quadriplegic, pentameter, and octopus.<br />Meanings? (words and prefixes)<br />
  28. 28. Polygons can be named by their number of sides.<br />
  29. 29. EQUIANGULAR POLYGON<br />EQUILATERAL POLYGON<br />REGULAR POLYGON<br />Concept Emphasis<br />
  30. 30. EQUILATERAL but not EQUIANGULAR<br />EQUILATERAL and EQUIANGULAR<br />┌<br />┌<br />┌<br />┌<br />EQUILATERAL and EQUIANGULAR<br />EQUILATERAL but not EQUIANGULAR<br />┌<br />┌<br />┌<br />┌<br />

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