不佳绘制的平行四边形(3)几何作图演示

不佳绘制的平行四边形(3)几何作图演示
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2024-05-04 21:50
本范例通过“不够精确的作图”来展示平行四边形在几何约束下仍可由点与线段关系生成的现象。核心概念包括:平行四边形的构成(由四点形成多边形)、线段与边的交点关系、以及通过作角度来刻画相对位置/方向的一致性。作图要点是利用 GeoGebra 的几何对象与基础几何工具:从构造摘要可提炼出使用了 Polygon(多边形)来生成四边形 ABCD;使用 Segment(线段)来建立各边或辅助边;使用 Intersect(求交)计算相关边的交点位置,从而保证形体的连接关系;并使用 Angle(角)来定义或显示关键角度约束。适合中学几何教学中的几何作图活动、平行四边形性质的直观理解,以及课堂/自学用于几何逻辑与作图步骤训练。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Segment(B, D) → f
  3. Segment(A, C) → g
  4. Intersect(f, g) → E
  5. Segment(A, E) → h
  6. Segment(E, C) → i
  7. Segment(E, D) → j
  8. Segment(E, B) → k
  9. Polygon(A_{1}, B_{1}, C_{1}, D_{1}) → q1_{1}, a_{1}, b_{1}, c_{1}, d_{1}
  10. Segment(B_{1}, D_{1}) → f_{1}
  11. Segment(A_{1}, C_{1}) → g_{1}
  12. Intersect(f_{1}, g_{1}) → E_{1}
  13. Segment(A_{1}, E_{1}) → h_{1}
  14. Segment(E_{1}, C_{1}) → i_{1}
  15. Segment(E_{1}, D_{1}) → j_{1}
  16. Segment(E_{1}, B_{1}) → k_{1}
  17. Polygon(A_{2}, B_{2}, C_{2}, D_{2}) → q1_{2}, a_{2}, b_{2}, c_{2}, d_{2}
  18. Segment(B_{2}, D_{2}) → f_{2}
  19. Segment(A_{2}, C_{2}) → g_{2}
  20. Intersect(f_{2}, g_{2}) → E_{2}
  21. Segment(A_{2}, E_{2}) → h_{2}
  22. Segment(E_{2}, C_{2}) → i_{2}
  23. Segment(E_{2}, D_{2}) → j_{2}
  24. Segment(E_{2}, B_{2}) → k_{2}
  25. Polygon(A_{3}, B_{3}, C_{3}, D_{3}) → q1_{3}, a_{3}, b_{3}, c_{3}, d_{3}
  26. Segment(B_{3}, D_{3}) → f_{3}
  27. Segment(A_{3}, C_{3}) → g_{3}
  28. Intersect(f_{3}, g_{3}) → E_{3}
  29. Segment(A_{3}, E_{3}) → h_{3}
  30. Segment(E_{3}, C_{3}) → i_{3}
  31. Segment(E_{3}, D_{3}) → j_{3}
  32. Segment(E_{3}, B_{3}) → k_{3}
  33. Polygon(A_{4}, B_{4}, C_{4}, D_{4}) → q1_{4}, a_{4}, b_{4}, c_{4}, d_{4}
  34. Segment(B_{4}, D_{4}) → f_{4}
  35. Segment(A_{4}, C_{4}) → g_{4}
  36. Intersect(f_{4}, g_{4}) → E_{4}
  37. Segment(A_{4}, E_{4}) → h_{4}
  38. Segment(E_{4}, C_{4}) → i_{4}
  39. Segment(E_{4}, D_{4}) → j_{4}
  40. Segment(E_{4}, B_{4}) → k_{4}
  41. Polygon(A_{5}, B_{5}, C_{5}, D_{5}) → q1_{5}, a_{5}, b_{5}, c_{5}, d_{5}
  42. Segment(B_{5}, D_{5}) → f_{5}
  43. Segment(A_{5}, C_{5}) → g_{5}
  44. Intersect(f_{5}, g_{5}) → E_{5}
  45. Segment(A_{5}, E_{5}) → h_{5}
  46. Segment(E_{5}, C_{5}) → i_{5}
  47. Segment(E_{5}, D_{5}) → j_{5}
  48. Segment(E_{5}, B_{5}) → k_{5}
  49. Polygon(A_{6}, B_{6}, C_{6}, D_{6}) → q1_{6}, a_{6}, b_{6}, c_{6}, d_{6}
  50. Segment(B_{6}, D_{6}) → f_{6}
  51. Segment(A_{6}, C_{6}) → g_{6}
  52. Intersect(f_{6}, g_{6}) → E_{6}
  53. Segment(A_{6}, E_{6}) → h_{6}
  54. Segment(E_{6}, C_{6}) → i_{6}
  55. Segment(E_{6}, D_{6}) → j_{6}
  56. Segment(E_{6}, B_{6}) → k_{6}
  57. Polygon(A_{7}, B_{7}, C_{7}, D_{7}) → q1_{7}, a_{7}, b_{7}, c_{7}, d_{7}
  58. Segment(B_{7}, D_{7}) → f_{7}
  59. Segment(A_{7}, C_{7}) → g_{7}
  60. Intersect(f_{7}, g_{7}) → E_{7}
  61. Segment(A_{7}, E_{7}) → h_{7}
  62. Segment(E_{7}, C_{7}) → i_{7}
  63. Segment(E_{7}, D_{7}) → j_{7}
  64. Segment(E_{7}, B_{7}) → k_{7}
  65. Angle(C_{3}, E_{3}, B_{3}) → α
  66. Angle(D_{3}, E_{3}, C_{3}) → β
  67. Angle(C_{7}, E_{7}, B_{7}) → γ
  68. Angle(D_{7}, E_{7}, C_{7}) → δ
  69. Polygon(A_{8}, B_{8}, C_{8}, D_{8}) → q1_{8}, a_{8}, b_{8}, c_{8}, d_{8}
  70. Segment(B_{8}, D_{8}) → f_{8}
  71. Segment(A_{8}, C_{8}) → g_{8}
  72. Intersect(f_{8}, g_{8}) → E_{8}
  73. Segment(A_{8}, E_{8}) → h_{8}
  74. Segment(E_{8}, C_{8}) → i_{8}
  75. Segment(E_{8}, D_{8}) → j_{8}
  76. Segment(E_{8}, B_{8}) → k_{8}
  77. Angle(C_{8}, E_{8}, B_{8}) → γ_{1}
  78. Angle(D_{8}, E_{8}, C_{8}) → δ_{1}
  79. Polygon(A_{9}, B_{9}, C_{9}, D_{9}) → q1_{9}, a_{9}, b_{9}, c_{9}, d_{9}
  80. Segment(B_{9}, D_{9}) → f_{9}
  81. Segment(A_{9}, C_{9}) → g_{9}
  82. Intersect(f_{9}, g_{9}) → E_{9}
  83. Segment(A_{9}, E_{9}) → h_{9}
  84. Segment(E_{9}, C_{9}) → i_{9}
  85. Segment(E_{9}, D_{9}) → j_{9}
  86. Segment(E_{9}, B_{9}) → k_{9}
  87. Angle(C_{9}, E_{9}, B_{9}) → γ_{2}
  88. Angle(D_{9}, E_{9}, C_{9}) → δ_{2}

AI 绘图提示语参考

要画一个平行四边形。选择四个点A、B、C、D。画出线段BD和AC,它们的交点记为E。然后从A到E、E到C、E到D、E到B依次连线,最后得到四边形ABCD。这个构造强调了通过交点E来连接各点,形成平行四边形的形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。