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Interior and Exterior Angles of Polygons by Steve Miller

Interior and Exterior Angles of Polygons by Steve Miller
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2016-01-06 23:10
PolygonAngleGeometric Construction
This example demonstrates the properties of interior and exterior angles of polygons, including the formula for the sum of interior angles and the theorem on the sum of exterior angles. It involves core mathematical concepts like angle calculations and polygon properties. Constructed using GeoGebra commands such as Segment, Angle, and Ray, with objects like points A_1 to A_8, sides, angles a_1 to a_8, and internal angles int_3 to int_8. Suitable for middle school and above students to explore polygon geometry, ideal for classroom demonstrations or self-directed learning.

GeoGebra Commands & Parameters

  1. Segment(A_1, A_2) → a_1
  2. Segment(A_2, A_3) → a_2
  3. Segment(A_3, A_1) → s_3
  4. Segment(A_3, A_4) → a_3
  5. Segment(A_4, A_1) → s_4
  6. Segment(A_4, A_5) → a_4
  7. Segment(A_5, A_1) → s_5
  8. Segment(A_5, A_6) → a_5
  9. Segment(A_6, A_1) → s_6
  10. Segment(A_6, A_7) → a_6
  11. Segment(A_7, A_1) → s_7
  12. Segment(A_7, A_8) → a_7
  13. Segment(A_8, A_1) → s_8
  14. Angle(A_3, A_2, A_1) → int_3
  15. Angle(A_1, A_3, A_2) → tempb_3
  16. Angle(A_2, A_1, A_3) → tempa_3
  17. Angle(A_4, A_3, A_2) → int_4
  18. Angle(A_1, A_4, A_3) → tempa_4
  19. Angle(A_2, A_1, A_4) → tempb_4
  20. Angle(A_5, A_4, A_3) → int_5
  21. Angle(A_1, A_5, A_4) → tempa_5
  22. Angle(A_2, A_1, A_5) → tempb_5
  23. Angle(A_6, A_5, A_4) → int_6
  24. Angle(A_1, A_6, A_5) → tempa_6
  25. Angle(A_2, A_1, A_6) → tempb_6
  26. Angle(A_7, A_6, A_5) → int_7
  27. Angle(A_1, A_7, A_6) → tempa_7
  28. Angle(A_2, A_1, A_7) → tempb_7
  29. Angle(A_8, A_7, A_6) → int_8
  30. Angle(A_1, A_8, A_7) → tempa_8
  31. Angle(A_2, A_1, A_8) → tempb_8
  32. Ray(A_1, A_2) → ray_1
  33. Ray(A_2, A_3) → ray_2
  34. Ray(A_3, A_1) → tempray_3
  35. Angle(tempray_3, a_1) → exttempa_3
  36. Angle(ray_1, a_2) → ext_1
  37. Angle(ray_2, s_3) → exttempb_3
  38. Ray(A_3, A_4) → ray_3
  39. Ray(A_4, A_1) → tempray_4
  40. Angle(ray_3, s_4) → exttempa_4
  41. Angle(tempray_4, a_1) → exttempb_4
  42. Angle(ray_2, a_3) → ext_4
  43. Ray(A_4, A_5) → ray_4
  44. Ray(A_5, A_1) → tempray_5
  45. Angle(ray_3, a_4) → ext_5
  46. Angle(ray_4, s_5) → exttempa_5
  47. Angle(tempray_5, a_1) → exttempb_5
  48. Angle(ray_4, a_5) → ext_6
  49. Ray(A_5, A_6) → ray_5
  50. Angle(ray_5, s_6) → exttempa_6
  51. Ray(A_6, A_1) → tempray_6
  52. Angle(tempray_6, a_1) → exttempb_6
  53. Angle(ray_5, a_6) → ext_7
  54. Ray(A_6, A_7) → ray_6
  55. Ray(A_7, A_1) → tempray_7
  56. Angle(ray_6, s_7) → exttempa_7
  57. Angle(tempray_7, a_1) → exttempb_7
  58. Ray(A_7, A_8) → ray_7
  59. Ray(A_8, A_1) → tempray_8
  60. Angle(ray_6, a_7) → ext_8
  61. Angle(ray_7, s_8) → exttempa_8
  62. Angle(tempray_8, a_1) → exttempb_8