1 / 45

POLYGONS

POLYGONS. WARM UP!!!. not a polygon. polygon. What is a polygon?. A polygon is a plane figure. A polygon is a closed region. A polygon is formed by three or more line segments as its sides. Each side of a polygon intersects only one segment at each of its endpoints. poli  “many angled”.

pavel
Download Presentation

POLYGONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. POLYGONS

  2. WARM UP!!!

  3. not a polygon polygon

  4. What is a polygon? • A polygon is a plane figure. • A polygon is a closed region. • A polygon is formed by three or more line segments as its sides. • Each side of a polygon intersects only one segment at each of its endpoints. • poli “many angled”

  5. Polygon or Not a Polygon?

  6. Polygon or Not a Polygon? Polygon

  7. Polygon or Not a Polygon?

  8. Polygon or Not a Polygon? Not Polygon because sides are not line segments.

  9. Polygon or Not a Polygon?

  10. Polygon or Not a Polygon? Not Polygon because sides are intersecting at more than the endpoints.

  11. Polygon or Not a Polygon?

  12. Polygon or Not a Polygon? Polygon

  13. Polygon or Not a Polygon?

  14. Polygon or Not a Polygon? Not Polygon because sides are not intersecting at the endpoints.

  15. Polygon or Not a Polygon?

  16. Polygon or Not a Polygon? Polygon

  17. Polygon or Not a Polygon?

  18. Polygon or Not a Polygon? Not Polygon because sides are intersecting more than one other side at its endpoint.

  19. Naming Polygons • 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. A B D C

  20. Polygons can be named by their number of sides.

  21. Connecting to Prior Knowledge • Think of words beginning with the prefixes tri-, quad-, pent-, and oct-. • Examples: triathlon, quadriplegic, pentameter, and octopus.

  22. Regions in a Polygon

  23. Parts of a Polygon • sides • consecutive sides • included angle • nonconsecutive sides • interior angles / vertex angles • consecutive angles • included side • nonconsecutive angles • exterior angles

  24. Interior Angles of Polygons • In a triangle the sum of the interior angles =180o • In a quadrilateral the sum of the interior angles =360o USING WHAT YOU KNOW ABOUT TRIANGLES PROVE IT!!

  25. Interior Angles of Polygons • Now how about a pentagon? • In a pentagon the sum of the interior angles =540o

  26. Interior Angles of Polygons • In any polygon, the sum of the interior angles is: 180 (sides – 2) • NOTE: sides-2 is equal to the number of triangles you can form in the interior of the polygon! • What is the sum of interior angles in a: • Hexagon – 720o • Octagon - 1080o • Decagon - 1440o

  27. ALL POLYGONS???

  28. ALL POLYGONS!

  29. How can these polygons be divided into two groups?

  30. Concave Polygons Convex Polygons

  31. 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.

  32. Convex or Concave? Convex

  33. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.

  34. Convex or Concave? Convex

  35. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

  36. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

  37. Convex or Concave? Convex

  38. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

  39. Concepts • EQUIANGULAR POLYGON • EQUILATERAL POLYGON • REGULAR POLYGON

  40. EQUILATERAL but not EQUIANGULAR EQUILATERAL and EQUIANGULAR ┌ ┌ ┌ ┌ EQUILATERAL and EQUIANGULAR EQUIANGULAR but not EQUILATERAL ┌ ┌ ┌ ┌

  41. Regular vs. Irregular polygons Which of these is a regular pentagon?

  42. Regular vs. Irregular polygons Regular polygons are equilateral and equiangular Examples??? Square, regular pentagon, equilateral triangle Counterexamples??? Kite, rhombus, trapezoid, parallelogram, isosceles triangle

  43. 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.

  44. Practice Exercise Set 6.1 on pages 280-282 #1-6, 9-12, 18, 19 • B. C. D.

  45. not a polygon polygon

More Related