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Exterior Angles of a Hexagon

Exterior Angles of a Hexagon
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2015-10-27 17:39
PolygonAngleGeometric Construction
In collections Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles Polygons & Angles Polygons & Angles
This example demonstrates the properties and calculation of exterior angles in a hexagon. It involves core mathematical concepts such as the sum of exterior angles theorem, angle measurement, and geometric construction. Key GeoGebra commands used include Circle, Point, Line, Rotate, Angle, CircleArc, Ray, Intersect, CircleSector, and Polygon. Suitable for middle school students and above learning polygon geometry or for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Circle(A, 8 - a) → c
  2. Point(c) → B
  3. Line(A, B) → b
  4. Rotate(B, 60°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 60°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 60°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 60°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 60°, A) → C'
  13. Angle(C, A, C') → ε
  14. CircleArc(A, B, B') → d
  15. CircleArc(A, B', B'') → e
  16. CircleArc(A, B'', B''') → f
  17. CircleArc(A, B''', C) → g
  18. CircleArc(A, C, C') → h
  19. CircleArc(A, C', B) → k
  20. Point(d) → D
  21. Point(e) → E
  22. Point(f) → F
  23. Point(g) → G
  24. Point(h) → H
  25. Point(k) → I
  26. Ray(D, E) → i
  27. Ray(E, F) → j
  28. Ray(F, G) → l
  29. Ray(G, H) → m
  30. Ray(H, I) → n
  31. Ray(I, D) → p
  32. Circle(E, 1.5) → q
  33. Circle(F, 1.5) → r
  34. Circle(G, 1.5) → s
  35. Circle(H, 1.5) → t
  36. Circle(I, 1.5) → c_1
  37. Circle(D, 1.5) → d_1
  38. Intersect(r, j, 1) → J
  39. Intersect(r, l, 1) → K
  40. Intersect(s, l, 2) → L
  41. Intersect(s, m, 1) → M
  42. Intersect(r, j, 2) → N
  43. Intersect(t, m, 2) → O
  44. Intersect(t, n, 1) → P
  45. Intersect(c_1, n, 2) → Q
  46. Intersect(c_1, p, 1) → R
  47. Intersect(d_1, p, 2) → S
  48. Intersect(d_1, i, 1) → T
  49. Intersect(q, j, 1) → U
  50. Intersect(q, i, 2) → V
  51. CircleSector(F, N, K) → e_1
  52. CircleSector(G, L, M) → f_1
  53. CircleSector(H, O, P) → g_1
  54. CircleSector(I, Q, R) → h_1
  55. CircleSector(D, S, T) → k_1
  56. CircleSector(E, V, U) → p_1
  57. Polygon(G, H, I, D, E, F) → poly1, g_2, h_2, i_1, d_2, e_2, f_2

AI Drawing Prompt Reference

Draw a hexagon, then rotate each vertex 60 degrees to form the exterior angles. Next, draw arcs for each exterior angle using circular arcs and circles. Finally, find points on the circumscribed circle of the hexagon through intersections to form the circumscribed circle.
The prompt above was compiled from the original drawing commands and is for reference only.