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Dynamic Quadrilateral Demo

Dynamic Quadrilateral Demo
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2017-01-27 11:33
TriangleCircleProbability & StatisticsGeometric ConstructionSlider Animation
This example dynamically illustrates the geometric relationships between a circumcircle and triangles within a quadrilateral. It involves core math concepts like line segments, interest calculation, combinatorics, circumcircle, and conditional probability. Construction highlights GeoGebra commands: Polygon, Midpoint, Segment, Line, OrthogonalLine, Intersect, Angle, Dilate, Rotate, Vector, and Translate. Suitable for high school mathematics students and educators for geometric construction and probability/statistics learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(B, E, 4) → poly2, j, k, l, m, F, G
  3. Midpoint(E, F) → H
  4. Segment(A, H) → n
  5. Segment(A, F) → p
  6. Segment(A, C) → q
  7. Segment(C, B) → r
  8. Line(A, C) → s
  9. OrthogonalLine(F, s) → t
  10. OrthogonalLine(D, q) → b
  11. OrthogonalLine(C, p) → c
  12. OrthogonalLine(H, p) → d
  13. Intersect(c, p) → I
  14. Intersect(d, p) → J
  15. Line(A, H) → e
  16. OrthogonalLine(F, e) → f_1
  17. OrthogonalLine(E, n) → g_1
  18. Intersect(e, g_1) → K
  19. Intersect(e, f_1) → L
  20. Intersect(b, q) → M
  21. Angle(C, M, D) → α
  22. Angle(C, I, A) → β
  23. Angle(H, J, F) → γ
  24. Intersect(s, t) → N
  25. Angle(C, N, F) → δ
  26. Angle(F, L, H) → ε
  27. Angle(A, K, E) → ζ
  28. Polygon(A, C, D) → poly3, d_1, a_1, c_1
  29. Polygon(A, F, C) → poly4, c_2, a_2, f_2
  30. Polygon(A, H, F) → poly5, f_3, a_3, h_1
  31. Polygon(A, E, H) → poly6, h_2, a_4, e_1
  32. Dilate(E, If[0 < o ≤ 1, 1 - o, 0], H) → E'
  33. Segment(E, E') → i_1
  34. Angle(F, E, B) → η
  35. Angle(D, F, E) → θ
  36. Angle(A, D, F) → ι
  37. Angle(E, A, D) → κ
  38. Rotate(E, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → E'_1
  39. Rotate(E', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → E''
  40. Segment(E'_1, E'') → j_1
  41. Dilate(F, If[2 < o ≤ 3, 3 - o, 0], G) → F'
  42. Rotate(E, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E'_2
  43. Rotate(E', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E''_1
  44. Rotate(E'_1, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → O
  45. Rotate(E'', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E'''
  46. Angle(D, C, B) → λ
  47. Angle(E, B, C) → μ
  48. Segment(A, E) → n_1
  49. Segment(D, A) → p_1
  50. Segment(D, C) → k_1
  51. Rotate(D, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], G) → D'
  52. Rotate(C, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], G) → C'
  53. Segment(D', C') → l_1
  54. Rotate(D', If[3 < o ≤ 4, ((o - 3) * π / 2), π / 2], G) → D''
  55. Rotate(C', If[3 < o ≤ 4, ((o - 3) * π / 2), π / 2], G) → C''
  56. Segment(D'', C'') → m_1
  57. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], G) → A'
  58. Segment(A, A') → q_1
  59. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], M) → D'_1
  60. Segment(D, D'_1) → r_1
  61. Dilate(G, If[5 < o ≤ 6, 6 - o, 0], N) → G'
  62. Dilate(F, If[5 < o ≤ 6, 6 - o, 0], N) → F'_1
  63. Segment(G, G') → s_1
  64. Segment(F, F'_1) → t_1
  65. Rotate(D, If[6 < o ≤ 7, ((o - 6) * π), π], G) → D'_2
  66. Rotate(D'_1, If[6 < o ≤ 7, ((o - 6) * π), π], G) → P
  67. Dilate(D, If[6 < o ≤ 7, 7 - o, 0], N) → D'_3
  68. Vector(D, D'_3) → u
  69. Translate(D, u) → D'_4
  70. Translate(D'_1, u) → Q
  71. Segment(D'_4, Q) → b_1
  72. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], F) → A'_1
  73. Segment(A, A'_1) → g_2
  74. Dilate(G, If[8 < o ≤ 9, 9 - o, 0], I) → G'_1
  75. Dilate(H, If[8 < o ≤ 9, 9 - o, 0], J) → H'
  76. Segment(G, G'_1) → i_2
  77. Segment(H, H') → j_2
  78. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], H) → A'_2
  79. Segment(A, A'_2) → k_2
  80. Dilate(G, If[9 < o ≤ 10, 10 - o, 0], J) → G'_2
  81. Vector(G, G'_2) → v
  82. Translate(G, v) → G'_3
  83. Translate(G'_1, v) → R
  84. Segment(G'_3, R) → l_2
  85. Dilate(H, If[10 < o ≤ 11, 11 - o, 0], L) → H'_1
  86. Dilate(F, If[10 < o ≤ 11, 11 - o, 0], L) → F'_2
  87. Segment(F, F'_2) → n_2
  88. Dilate(E, If[10 < o ≤ 11, 11 - o, 0], K) → E'_3
  89. Segment(E, E'_3) → m_2
  90. Segment(H, H'_1) → p_2
  91. Dilate(L, If[11 < o ≤ 12, 12 - o, 0], E) → L'
  92. Vector(L, L') → w
  93. Translate(F, w) → F'_3
  94. Translate(F'_2, w) → S
  95. Segment(F'_3, S) → q_2
  96. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], G) → D'_5
  97. Segment(D, D'_5) → r_2