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日常中的平行四边形：性质识别与自由作图练习

日常中的平行四边形：性质识别与自由作图练习
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2023-12-06 20:39
多边形角向量几何作图
所属专题 Parallelogramm und Raute: Eigenschaften und Konstruktionen
该范例通过互动任务引导学习者在日常情境中发现平行四边形，并完成任意大小平行四边形的草图与实例收集。核心数学概念包括：平行四边形作为特殊四边形的判别与性质应用（如对边平行、对边长度与角的对应关系）、多边形建构，以及在几何环境中通过点与边的约束来生成图形。作图与交互要点来源于构造摘要：使用 Textfield 设置输入/提示文本；以 Point 生成顶点并用 Polygon 连接形成四边形；结合 Midpoint、Distance 计算关键几何量；通过 Element、IndexOf、Min 参与对象选择/索引与约束取值；用 Zip、Join 管理对象集合；并借助多种对象（如 PStart、PCurrent、moved 以及多组点 A3/B3…A6/B6）与步进参数（step、maxstep、resx、resy）实现可拖拽与逐步呈现。适合5-6年级到初中入门几何、课堂互动探究或作业巩固，用于培养描述与应用特殊四边形性质的能力。

GeoGebra 命令及参数

  1. Textfield(input1) → Eingabefeld1
  2. Textfield(input2) → Eingabefeld2
  3. Polygon(Sequence[Rotate[PCenter + (spyRadius - 0.05, 0), K, PCenter], K, 0, 360°, 0.5]) → spyGlass
  4. Point(Line[PCurrent, xAxis]) → PCurrent2
  5. Midpoint(B2, C2) → D2
  6. Midpoint(B3, C3) → D3
  7. Midpoint(B4, C4) → D4
  8. Midpoint(B5, C5) → D5
  9. Midpoint(B6, C6) → D6
  10. Midpoint(B7, C7) → D7
  11. Midpoint(B8, C8) → D8
  12. Midpoint(B9, C9) → D9
  13. Midpoint(B10, C10) → D10
  14. Midpoint(B11, C11) → D11
  15. Midpoint(B12, C12) → D12
  16. Midpoint(B13, C13) → D13
  17. Midpoint(B14, C14) → D14
  18. Midpoint(B15, C15) → D15
  19. Midpoint(B16, C16) → D16
  20. Midpoint(B17, C17) → D17
  21. Distance(D2, PCenter) → E2
  22. Distance(D3, PCenter) → E3
  23. Distance(D4, PCenter) → E4
  24. Distance(D5, PCenter) → E5
  25. Distance(D6, PCenter) → E6
  26. Distance(D7, PCenter) → E7
  27. Distance(D8, PCenter) → E8
  28. Distance(D9, PCenter) → E9
  29. Distance(D10, PCenter) → E10
  30. Distance(D11, PCenter) → E11
  31. Distance(D12, PCenter) → E12
  32. Distance(D13, PCenter) → E13
  33. Distance(D14, PCenter) → E14
  34. Distance(D15, PCenter) → E15
  35. Distance(D16, PCenter) → E16
  36. Distance(D17, PCenter) → E17
  37. Element({CellRange(E1,E17,"numeric"), CellRange(E21,E30,"numeric"), CellRange(E31,E49,"numeric")}, exnum) → distancesCurrent
  38. IndexOf(Min[distancesCurrent], distancesCurrent) → displayIndex
  39. Min(Distance[D1, PCenter], Distance[F1, PCenter]) → E1
  40. Midpoint(B20, C20) → D20
  41. Midpoint(B21, C21) → D21
  42. Midpoint(B22, C22) → D22
  43. Midpoint(B23, C23) → D23
  44. Midpoint(B24, C24) → D24
  45. Midpoint(B25, C25) → D25
  46. Midpoint(B26, C26) → D26
  47. Distance(D21, PCenter) → E21
  48. Distance(D22, PCenter) → E22
  49. Distance(D23, PCenter) → E23
  50. Distance(D24, PCenter) → E24
  51. Distance(D25, PCenter) → E25
  52. Distance(D26, PCenter) → E26
  53. Min(Zip[Distance[A, PCurrent], A, currLocationsA20]) → E20
  54. Zip(Z ≤ tolerance, Z, distancesCurrent) → distanceCheck
  55. Element({CellRange(A1,A17,"point"), CellRange(A21,A30,"point"), CellRange(A31,A49,"point")}, exnum) → allPointsA
  56. Element({CellRange(B1,B17,"point"), CellRange(B21,B30,"point"), CellRange(B31,B49,"point")}, exnum) → allPointsB
  57. Element({CellRange(C1,C17,"point"), CellRange(C21,C30,"point"), CellRange(C31,C49,"point")}, exnum) → allPointsC
  58. Zip(Polygon[M, N, O, O + Vector[N, M]], M, allPointsC, N, allPointsA, O, allPointsB) → allParallelograms
  59. Zip(IntersectPath[Z, spyGlass], Z, allParallelograms) → allVisibleParallels
  60. Midpoint(B27, C27) → D27
  61. Midpoint(B28, C28) → D28
  62. Midpoint(B29, C29) → D29
  63. Midpoint(B30, C30) → D30
  64. Distance(D27, PCenter) → E27
  65. Distance(D28, PCenter) → E28
  66. Distance(D29, PCenter) → E29
  67. Distance(D30, PCenter) → E30
  68. Midpoint(B31, C31) → D31
  69. Midpoint(B32, C32) → D32
  70. Midpoint(B33, C33) → D33
  71. Midpoint(B34, C34) → D34
  72. Midpoint(B35, C35) → D35
  73. Midpoint(B36, C36) → D36
  74. Midpoint(B37, C37) → D37
  75. Midpoint(B38, C38) → D38
  76. Midpoint(B39, C39) → D39
  77. Midpoint(B40, C40) → D40
  78. Midpoint(B41, C41) → D41
  79. Midpoint(B42, C42) → D42
  80. Midpoint(B43, C43) → D43
  81. Midpoint(B44, C44) → D44
  82. Midpoint(B45, C45) → D45
  83. Midpoint(B46, C46) → D46
  84. Midpoint(B47, C47) → D47
  85. Midpoint(B48, C48) → D48
  86. Midpoint(B49, C49) → D49
  87. Distance(D31, PCenter) → E31
  88. Distance(D32, PCenter) → E32
  89. Distance(D33, PCenter) → E33
  90. Distance(D34, PCenter) → E34
  91. Distance(D35, PCenter) → E35
  92. Distance(D36, PCenter) → E36
  93. Distance(D37, PCenter) → E37
  94. Distance(D38, PCenter) → E38
  95. Distance(D39, PCenter) → E39
  96. Distance(D40, PCenter) → E40
  97. Distance(D41, PCenter) → E41
  98. Distance(D42, PCenter) → E42
  99. Distance(D43, PCenter) → E43
  100. Distance(D44, PCenter) → E44
  101. Distance(D45, PCenter) → E45
  102. Distance(D46, PCenter) → E46
  103. Distance(D47, PCenter) → E47
  104. Distance(D48, PCenter) → E48
  105. Distance(D49, PCenter) → E49
  106. Element({CellRange(D1,D17,"point"), CellRange(D21,D30,"point"), CellRange(D31,D49,"point")}, exnum) → currLocations
  107. Join(Sequence[Shuffle[{1, 2, 3}], m, 1, 35]) → listExnum

AI 绘图提示语参考

画一个任意大小的平行四边形，标出关键顶点，并计算各边中点和中心点之间的距离。用不同颜色或线型突出显示对边平行和对应边角关系。展示多个边中点，并按距离从中心点最近到最远排序，用文本框输入参数并动态调整图形大小和显示的边中点数量。
以上提示语为根据原始绘图命令整理而来，仅供参考。