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GoGeometry Action 156! Dynamic Quadrilateral Rotation and Probability

GoGeometry Action 156! Dynamic Quadrilateral Rotation and Probability
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2018-06-24 12:30
PolygonFunctionProbability & StatisticsTransformationGeometric Construction
This interactive GeoGebra example dynamically illustrates problem 156 from GoGeometry, featuring a general quadrilateral under rotation and translation, with connections to probability and function graphs. The core mathematical concepts include properties of general quadrilaterals, rotation transformations, midpoints, angle bisectors, circles and arcs, function graphing, and probabilistic interpretations. The construction uses GeoGebra commands such as Rotate, Translate, Dilate for transformations; Point, Segment, LineBisector, Intersect, Circle, Angle, Ray, Midpoint, Polygon, CircleSector, Vector for geometric objects; and Min, Function Graph for generating curves. Suitable for high school and above, this resource supports exploration of geometric transformations, dynamic geometry, and integrated probability problems, ideal for classroom demonstrations or self-directed learning.

GeoGebra Commands & Parameters

  1. Rotate(C, π / 3, A) → B
  2. Segment(B, C) → i
  3. Point(i) → D
  4. LineBisector(A, D) → j
  5. LineBisector(D, B) → k
  6. Intersect(j, k) → C_1
  7. Circle(C_1, D) → d
  8. Angle(C, A, D) → α
  9. Rotate(C, α / 2, A) → C'
  10. Ray(A, C') → l
  11. Intersect(d, l) → F_1, F
  12. Ray(D, F) → m
  13. Segment(A, C) → n
  14. Intersect(m, n) → G
  15. Midpoint(G, C) → Q
  16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], C) → A'
  17. Segment(A, A') → f
  18. Rotate(G, π / 3, F) → G'
  19. Ray(F, G') → j_1
  20. Intersect(f, j_1) → M
  21. Midpoint(F, M) → O
  22. Midpoint(O, M) → P
  23. Polygon(A, C, B) → t1, b', a, b
  24. Rotate(C, If[1 < c ≤ 2, ((c - 1) * π / 3), π / 3], A) → B'_1
  25. Segment(A, B'_1) → g
  26. Rotate(A, If[2 < c ≤ 3, ((c - 2) * π / 3), π / 3], B) → A'_1
  27. Segment(B, A'_1) → h
  28. Angle(C, A, C') → β
  29. Intersect(h, l) → E
  30. Intersect(d, n) → H, I
  31. Circle(A, (0.6 * Distance[A, I])) → e
  32. Intersect(e, n) → J,
  33. Dilate(C_1, If[6 < c ≤ 7, 7 - c, 0], B) → K
  34. Circle(C_1, K) → p
  35. Segment(C_1, K) → q
  36. Segment(A, F) → r
  37. Dilate(A, If[8 < c ≤ 9, 9 - c, 0], D) → A'_2
  38. Segment(A, A'_2) → s
  39. Rotate(J, If[9 < c ≤ 10, ((c - 9) * β), β], A) → J'
  40. Dilate(A, If[9 < c ≤ 10, 10 - c, 0], F) → A'_3
  41. Segment(A, A'_3) → t
  42. CircleSector(A, J, J') → c_1
  43. Dilate(F, If[10 < c ≤ 11, 11 - c, 0], E) → F'
  44. Segment(F, F') → f_1
  45. Rotate(c_1, If[11 < c ≤ 12, ((c - 11) * β), β], A) → d_1
  46. Dilate(D, If[12 < c ≤ 13, 13 - c, 0], F) → D'
  47. Segment(D, D') → g_1
  48. Dilate(F, If[13 < c ≤ 14, 14 - c, 0], G) → F'_1
  49. Segment(F, F'_1) → h_1
  50. Angle(B, F, A) → γ
  51. Angle(G, F, E) → δ
  52. Rotate(A, If[15 < c ≤ 16, ((-(c - 15)) * γ), (-γ)], F) → A'_4
  53. Rotate(A'_3, If[15 < c ≤ 16, ((-(c - 15)) * γ), (-γ)], F) → L
  54. Segment(A'_4, L) → t'
  55. Rotate(F, If[16 < c ≤ 17, (((-(c - 16)) * 2) * π / 3), (-2 * π / 3)], F) → F'_2
  56. Rotate(F', If[16 < c ≤ 17, (((-(c - 16)) * 2) * π / 3), (-2 * π / 3)], F) → F''
  57. Segment(F'_2, F'') → i_1
  58. Angle(G, F, G') → ε
  59. Min({Distance[E, C], Distance[G, C], f_1}) → o
  60. Circle(C, (0.6 * o)) → e_1
  61. Intersect(e_1, h, 1) → N
  62. Rotate(N, If[17 < c ≤ 18, ((c - 17) * π / 3), π / 3], C) → N'
  63. Dilate(F, If[17 < c ≤ 18, 18 - c, 0], P) → F'_3
  64. CircleSector(C, N, N') → k_1
  65. Dilate(C, If[19 < c ≤ 20, 20 - c, 0], Q) → C'_1
  66. Segment(F, F'_3) → l_1
  67. Vector(C, C'_1) → u
  68. Translate(k_1, u) → p_1
  69. Line(C, l_1) → m_1
  70. Point(m_1) → R
  71. Angle(A, C, R) → ζ
  72. Rotate(p_1, If[20 < c ≤ 21, ((c - 20) * ζ), ζ], Q) → q_1
  73. Dilate(Q, If[21 < c ≤ 22, 22 - c, 0], F) → Q'
  74. Vector(Q, Q') → v
  75. Translate(q_1, v) → r_1
  76. Rotate(r_1, If[23 < c ≤ 24, ((c - 23) * π / 3), π / 3], F) → s_1