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Sum of Exterior Angles of Polygon

Sum of Exterior Angles of Polygon
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2017-02-17 15:44
PolygonAngleGeometric Construction
This example demonstrates the constant sum property of exterior angles in any polygon. Key math concepts include exterior angles, polygon interior angle sum theorem, and angle measurement. Construction highlights involve using GeoGebra commands like Ray, Angle, Translate, and Segment to build polygons and their exterior angles. Suitable for middle school and above mathematics learners for visualizing the theorem and its applications.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Ray(B, C) → b
  3. Ray(C, D) → c
  4. Ray(D, E) → d
  5. Ray(E, F) → e
  6. Ray(F, G) → f
  7. Ray(G, H) → g
  8. Ray(H, A) → h
  9. Angle(f, g) → α
  10. Angle(g, h) → β
  11. Angle(h, a) → γ
  12. Angle(a, b) → δ
  13. Angle(b, c) → ε
  14. Angle(c, d) → ζ
  15. Angle(d, e) → η
  16. Angle(e, f) → θ
  17. Translate(H, u) → H'
  18. Translate(A, u) → A'
  19. Ray(H', A') → h'
  20. Translate(A, v) → A'_1
  21. Translate(B, v) → B'
  22. Ray(A'_1, B') → a'
  23. Translate(B, w) → B'_1
  24. Translate(C, w) → C'
  25. Ray(B'_1, C') → b'
  26. Translate(C, r) → C'_1
  27. Translate(D, r) → D'
  28. Ray(C'_1, D') → c'
  29. Translate(D, s) → D'_1
  30. Translate(E, s) → E'
  31. Ray(D'_1, E') → d'
  32. Translate(E, t) → E'_1
  33. Translate(F, t) → F'
  34. Ray(E'_1, F') → e'
  35. Translate(F, u_1) → F'_1
  36. Translate(G, u_1) → G'
  37. Ray(F'_1, G') → f'
  38. Translate(G, v_1) → G'_1
  39. Translate(H, v_1) → H'_1
  40. Ray(G'_1, H'_1) → g'
  41. Angle(h', a') → ι
  42. Angle(a', b') → κ
  43. Angle(b', c') → λ
  44. Angle(c', d') → μ
  45. Angle(d', e') → ν
  46. Angle(e', f') → ξ
  47. Angle(f', g') → ο
  48. Angle(g', h') → ρ
  49. Segment(B'_1, A'_1) → i
  50. Segment(A'_1, H') → j
  51. Segment(H', G'_1) → k
  52. Segment(G'_1, F'_1) → l
  53. Segment(F'_1, E'_1) → m
  54. Segment(E'_1, D'_1) → n
  55. Segment(D'_1, C'_1) → p
  56. Segment(C'_1, B'_1) → q