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Pentagon Exterior Angles Exploration

Pentagon Exterior Angles Exploration
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2017-06-15 08:16
PolygonAngleGeometric Construction
This example demonstrates the properties and calculation of exterior angles in a pentagon, covering core concepts like the sum of exterior angles theorem and the relationship between interior and exterior angles. It is constructed using GeoGebra commands such as Ray, Rotate, Angle, Point, Line, Circle, Intersect, Segment, and Polygon, making it suitable for middle school and above students to understand polygonal geometry and dynamic geometric transformations.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(A, α, B) → A'
  3. Angle(A, B, A') → β
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Line(C, f) → h
  7. Circle(C, 2) → c
  8. Intersect(c, h) → D, E
  9. Intersect(c, g, 2) → F
  10. Ray(C, A) → i
  11. Angle(B, C, A) → γ
  12. Rotate(B, δ, C) → B'
  13. Angle(B, C, B') → ε
  14. Ray(C, B') → j
  15. Line(A, g) → k
  16. Intersect(k, j) → H
  17. Segment(C, H) → l
  18. Point(l) → G
  19. Line(G, g) → m
  20. Line(B, A) → n
  21. Intersect(m, n) → I
  22. Angle(C, G, I) → ζ
  23. Rotate(C, η, G) → C'
  24. Angle(C, G, C') → θ_1
  25. Ray(G, C') → p
  26. Intersect(n, p) → J
  27. Segment(G, J) → q
  28. Point(q) → K
  29. Ray(K, A) → r
  30. Line(C, G) → s
  31. Line(G, K) → t
  32. Line(K, A) → a
  33. Line(B, C) → b
  34. Segment(B, C) → d
  35. Segment(C, G) → e
  36. Segment(G, K) → f_1
  37. Segment(K, A) → g_1
  38. Segment(A, B) → h_1
  39. Min({d, e, f_1, g_1, h_1}) → o
  40. Circle(B, (0.3 * o)) → c_1
  41. Circle(C, (0.3 * o)) → d_1
  42. Circle(G, (0.3 * o)) → e_1
  43. Circle(K, (0.3 * o)) → k_1
  44. Circle(A, (0.3 * o)) → p_1
  45. Intersect(c_1, n) → L, M
  46. Intersect(c_1, b) → N, O
  47. Intersect(d_1, b) → P, Q
  48. Intersect(d_1, s) → R, S
  49. Intersect(e_1, t) → T, U
  50. Intersect(e_1, s) → V, W
  51. Intersect(k_1, t) → Z, A_1
  52. Intersect(k_1, a) → B_1, C_1
  53. Intersect(p_1, n) → D_1, E_1
  54. Intersect(p_1, a) → F_1, G_1
  55. Line(G, A) → i_1
  56. CircleSector(B, O, L) → q_1
  57. CircleSector(C, S, Q) → r_1
  58. CircleSector(A, D_1, G_1) → c_2
  59. CircleSector(K, C_1, A_1) → t_1
  60. CircleSector(G, U, W) → s_1
  61. Polygon(B, A, K, G, C) → poly1, b_1, a_1, k_2, g_2, c_3
  62. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'_1
  63. Vector(A, A'_1) → v
  64. Translate(c_2, v) → d_2
  65. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], C) → B'_1
  66. Vector(B, B'_1) → w
  67. Translate(q_1, w) → e_2
  68. Translate(d_2, w) → f_2
  69. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], G) → C'_1
  70. Vector(C, C'_1) → u_1
  71. Translate(e_2, u_1) → h_2
  72. Translate(f_2, u_1) → p_2
  73. Translate(r_1, u_1) → q_2
  74. Dilate(G, If[3 < u ≤ 4, 4 - u, 0], K) → G'
  75. Vector(G, G') → v_1
  76. Translate(q_2, v_1) → r_2
  77. Translate(s_1, v_1) → s_2
  78. Translate(h_2, v_1) → t_2
  79. Translate(p_2, v_1) → d_3
  80. CircleArc(A, D_1, G_1) → e_3
  81. CircleArc(B, O, L) → f_3
  82. CircleArc(C, S, Q) → g_3
  83. CircleArc(G, U, W) → h_3