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GoGeometry 行动47：平行四边形动态几何演示

GoGeometry 行动47：平行四边形动态几何演示
几何画板及绘图内容加载中，请稍等……
2017-05-21 09:56
多边形角变换几何作图滑块动画
① 本范例动态展示了一个与平行四边形相关的几何问题，源自GoGeometry网站，通过可拖拽的交互图形直观呈现几何关系。② 核心数学概念涉及平行四边形性质、线段比例、角度关系以及切线等，并可能包含整数边长或指数运算的趣味设定。③ 作图要点：从构造摘要可见，使用了射线、旋转、直线、点、交点、线段、角、圆、位似、扇形、向量、平移、多边形、中点、垂线等GeoGebra命令，构建了丰富的辅助线与动态对象，如A、B、C、D等点以及多个圆和线段，支持实时修改与观察。④ 适合中学几何教学或自学，用于探索平行四边形相关定理，也可作为动态几何课件设计的参考范例。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Rotate(B, a°, A) → B'
  3. Ray(A, B') → g
  4. Line(B, g) → h
  5. Point(g) → C
  6. Line(C, f) → i
  7. Intersect(h, i) → D
  8. Segment(C, D) → g_3
  9. Line(A, D) → t_1
  10. Segment(A, C) → f_3
  11. Angle(B, A, B') → α
  12. Segment(C, D) → j
  13. Segment(A, B) → k
  14. Segment(B, D) → l
  15. Segment(A, C) → m
  16. Min(m, k) → b
  17. Circle(C, (0.2 * b)) → d
  18. Circle(A, (0.2 * b)) → e
  19. Circle(B, (0.2 * b)) → p
  20. Circle(D, (0.2 * b)) → c
  21. Intersect(e, k, 1) → E
  22. Intersect(e, m, 1) → F
  23. Intersect(p, k, 1) → G
  24. Intersect(p, l, 1) → H
  25. Intersect(d, g, 2) → I
  26. Ray(C, I) → q
  27. Intersect(c, h, 2) → J
  28. Ray(D, J) → r
  29. Intersect(c, i, 2) → K
  30. Ray(D, K) → s
  31. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  32. Segment(A, A') → t
  33. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  34. CircleSector(A, E, E') → c_1
  35. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  36. Vector(A, A'_1) → u
  37. Translate(c_1, u) → d_1
  38. Segment(A, A'_1) → f_1
  39. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  40. Vector(C, C') → v
  41. Translate(d_1, v) → e_1
  42. Segment(C, C') → g_1
  43. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  44. Segment(D, D') → h_1
  45. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  46. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  47. Vector(A, A'_2) → w
  48. Translate(A, w) → A'_3
  49. Translate(A', w) → A''
  50. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  51. Vector(A, A'_4) → u_1
  52. Translate(A, u_1) → A'_5
  53. Translate(A'_1, u_1) → L
  54. Rotate(D, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → D'_2
  55. Rotate(D', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → D''
  56. Rotate(C, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → C'_2
  57. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → C''
  58. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → A'_7
  59. Rotate(A'_1, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → M
  60. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A'_8
  61. Rotate(A', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A''_1
  62. Rotate(D, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → D'_3
  63. Rotate(D', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → D''_1
  64. Rotate(C, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → C'_3
  65. Rotate(C', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → C''_1
  66. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → A'_9
  67. Rotate(A'_1, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → N
  68. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → A'_{10}
  69. Rotate(A', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → A''_2
  70. Line(A, D) → s_2
  71. Midpoint(A, D) → Q
  72. Rotate(A, If[16 < o ≤ 17, ((o - 16) * π), π], Q) → A'_{11}
  73. Midpoint(A, C) → O
  74. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], O) → A'_6
  75. Segment(A, A'_6) → i_1
  76. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π), π], O) → A'_{12}
  77. Rotate(A'_6, If[7 < o ≤ 8, ((o - 7) * π), π], O) → P
  78. Segment(A'_{12}, P) → j_1
  79. Line(A, D) → k_1
  80. OrthogonalLine(B, k_1) → l_1
  81. Line(O, D) → m_1
  82. OrthogonalLine(B, m_1) → n_1
  83. Intersect(m_1, n_1) → R
  84. Dilate(O, If[8 < o ≤ 9, 9 - o, 0], D) → O'
  85. Segment(O, O') → p_1
  86. Dilate(B, If[9 < o ≤ 10, 10 - o, 0], R) → B'_1
  87. Segment(B, B'_1) → q_1
  88. Angle(B, R, D) → β
  89. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], R) → A'_{13}
  90. Segment(A, A'_{13}) → r_1
  91. Angle(B, A, R) → γ
  92. Rotate(A, If[11.5 < o ≤ 12.5, ((-(o - 11.5)) * γ), (-γ)], A) → A'_{14}
  93. Rotate(A'_{13}, If[11.5 < o ≤ 12.5, ((-(o - 11.5)) * γ), (-γ)], A) → S
  94. Segment(A'_{14}, S) → s_1
  95. Line(O, D) → f_2
  96. Circle(D, 2) → e_2
  97. Circle(O, 2) → g_2
  98. Intersect(e_2, f_2, 2) → T
  99. Intersect(g_2, f_2, 1) → U
  100. Ray(D, T) → h_2
  101. Ray(O, U) → i_2
  102. Polygon(R, B, D, C, A) → poly2, r_2, b_2, d_3, c_3, a_2
  103. Polygon(R, B, A) → poly3, a_3, r_3, b_3