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Dynamic Quadrilateral and Incircle Demonstration

Dynamic Quadrilateral and Incircle Demonstration
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2017-09-09 23:41
CirclePolygonProbability & StatisticsGeometric ConstructionSlider Animation
This example dynamically illustrates the relationship between quadrilaterals and incircles, allowing parameter adjustments to observe geometric transformations. Core concepts include parallelograms, squares, incircles, piecewise functions, random experiments, histograms, and isosceles triangles. Construction involves commands like Polygon, Segment, Rotate, Angle, Ray, Intersect, Line, Mirror, Dilate, Vector, Translate, and Point. Suitable for high school mathematics education, combining geometric transformations with statistical probability.

GeoGebra Commands & Parameters

  1. Polygon(B, B_2, 4) → poly1, f, g, h, i, C, B_1
  2. Polygon(C, C_2, 4) → poly2, j, k, l, m, D, C_1
  3. Polygon(A_2, B, 4) → poly3, n, p, q, r, A_1, A
  4. Segment(A, D) → s
  5. Rotate(D, π / 4, A) → D'
  6. Angle(D, A, D') → α
  7. Rotate(A, (-(π / 4)), D) → A'
  8. Angle(A', D, A) → β
  9. Ray(A, D') → t
  10. Ray(D, A') → a
  11. Intersect(t, a) → D_2
  12. Line(A, D) → b
  13. Mirror(D_2, b) → D_1
  14. Polygon(D_2, A, 4) → poly4, c, d, e, f_1, F, G
  15. Segment(A_1, D_2) → g_1
  16. Segment(D_2, C_1) → h_1
  17. Segment(C_1, B_2) → i_1
  18. Segment(B_2, A_1) → j_1
  19. Segment(B_1, A_2) → k_1
  20. Segment(A_2, D_1) → l_1
  21. Segment(D_1, C_2) → m_1
  22. Segment(C_2, B_1) → n_1
  23. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], B_2) → B'
  24. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], A_2) → B'_1
  25. Segment(B, B') → p_1
  26. Segment(B, B'_1) → q_1
  27. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B_2) → B'_2
  28. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B_2) → B''
  29. Segment(B'_2, B'') → r_1
  30. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B) → B'_3
  31. Rotate(B'_1, If[1 < o ≤ 2, ((-(o - 1)) * π / 2), ((-π)) / 2], B) → E
  32. Segment(B'_3, E) → s_1
  33. Rotate(B'_2, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], C) → H
  34. Rotate(B'', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], C) → B'''
  35. Segment(H, B''') → t_1
  36. Rotate(B'_3, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], A_1) → I
  37. Rotate(E, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], A_1) → E'
  38. Segment(I, E') → a_1
  39. Rotate(H, If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], B_1) → H'
  40. Rotate(B''', If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], B_1) → J
  41. Segment(H', J) → b_1
  42. Rotate(I, If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], A) → I'
  43. Rotate(E', If[3 < o ≤ 4, ((-(o - 3)) * π / 2), ((-π)) / 2], A) → E''
  44. Segment(I', E'') → c_1
  45. Angle(C, B_2, B) → γ
  46. Angle(B_1, C, B_2) → ε
  47. Angle(B, B_1, C) → δ
  48. Angle(A_1, B, A_2) → ζ
  49. Angle(A, A_1, B) → η
  50. Angle(A_2, A, A_1) → θ
  51. Dilate(C_2, If[5 < o ≤ 6, 6 - o, 0], C) → K
  52. Segment(C_2, K) → d_1
  53. Rotate(C_2, If[6 < o ≤ 7, ((o - 6) * π / 2), π / 2], C) → L
  54. Rotate(K, If[6 < o ≤ 7, ((o - 6) * π / 2), π / 2], C) → K'
  55. Segment(L, K') → e_1
  56. Rotate(L, If[7 < o ≤ 8, ((o - 7) * π / 2), π / 2], C_1) → L'
  57. Rotate(K', If[7 < o ≤ 8, ((o - 7) * π / 2), π / 2], C_1) → K''
  58. Segment(L', K'') → f_2
  59. Rotate(L', If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], D) → L''
  60. Rotate(K'', If[8 < o ≤ 9, ((o - 8) * π / 2), π / 2], D) → K'''
  61. Segment(L'', K''') → g_2
  62. Angle(C_2, C, C_1) → ι
  63. Angle(C, C_1, D) → κ
  64. Angle(C_1, D, C_2) → λ
  65. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], D_2) → A'_1
  66. Segment(A, A'_1) → h_2
  67. Rotate(A, If[10 < o ≤ 11, ((-(o - 10)) * π / 2), ((-π)) / 2], A) → A'_3
  68. Rotate(A'_1, If[10 < o ≤ 11, ((-(o - 10)) * π / 2), ((-π)) / 2], A) → M
  69. Segment(A'_3, M) → i_2
  70. Angle(D_1, A, D_2) → μ
  71. Dilate(A, If[11 < o ≤ 12, 12 - o, 0], D_1) → A'_2
  72. Vector(A, A'_2) → u
  73. Translate(A, u) → A'_4
  74. Translate(A'_1, u) → N
  75. Segment(A'_4, N) → j_2
  76. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], D_2) → A'_5
  77. Vector(A, A'_5) → v
  78. Translate(A'_3, v) → O
  79. Translate(M, v) → M'
  80. Segment(O, M') → k_2
  81. Dilate(A_1, If[15 < o ≤ 16, 16 - o, 0], D_2) → P
  82. Segment(A_1, P) → l_2
  83. Dilate(D_2, If[16 < o ≤ 17, 17 - o, 0], C_1) → Q
  84. Segment(D_2, Q) → m_2
  85. Dilate(D_2, If[17 < o ≤ 18, 18 - o, 0], C_1) → R
  86. Vector(D_2, R) → w
  87. Translate(A_1, w) → S
  88. Translate(P, w) → P'
  89. Segment(S, P') → n_2
  90. Dilate(D_2, If[18 < o ≤ 19, 19 - o, 0], A_1) → T
  91. Vector(D_2, T) → u_1
  92. Translate(D_2, u_1) → U
  93. Translate(Q, u_1) → Q'
  94. Segment(U, Q') → p_2
  95. Polygon(A_1, D_2, C_1, B_2) → poly5, a_2, d_2, c_2, b_2
  96. Dilate(B_1, If[19 < o ≤ 20, 20 - o, 0], A_2) → V
  97. Segment(B_1, V) → q_2
  98. Dilate(D_1, If[19 < o ≤ 20, 20 - o, 0], A_2) → W
  99. Segment(D_1, W) → r_2
  100. Dilate(A_2, If[20 < o ≤ 21, 21 - o, 0], B_1) → Z
  101. Vector(A_2, Z) → v_1
  102. Translate(D_1, v_1) → E_1
  103. Translate(W, v_1) → W'
  104. Segment(E_1, W') → s_2
  105. Dilate(B_1, If[21 < o ≤ 22, 22 - o, 0], C_2) → F_1
  106. Vector(B_1, F_1) → w_1
  107. Translate(B_1, w_1) → G_1
  108. Translate(V, w_1) → V'
  109. Segment(G_1, V') → t_2
  110. Polygon(C_2, D_1, A_2, B_1) → poly6, c_3, d_3, a_3, b_3
  111. Line(B_2, r_2) → e_2
  112. Point(e_2) → H_1
  113. Dilate(A_2, If[23 < o ≤ 24, 24 - o, 0], B_2) → I_1
  114. Vector(A_2, I_1) → u_2
  115. Translate(C_2, u_2) → J_1
  116. Translate(D_1, u_2) → K_1
  117. Translate(A_2, u_2) → L_1
  118. Translate(B_1, u_2) → M_1
  119. Polygon(J_1, K_1, L_1, M_1) → poly6', j_3, k_3, l_3, m_3
  120. Rotate(J_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → P_1
  121. Rotate(K_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → Q_1
  122. Rotate(L_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → R_1
  123. Rotate(M_1, If[24 < o ≤ 25, ((o - 24) * π / 2), π / 2], B_2) → S_1
  124. Polygon(P_1, Q_1, R_1, S_1) → poly6'', p_3, q_3, r_3, s_3