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请求一个直角三角形

请求一个直角三角形
几何画板及绘图内容加载中，请稍等……
2025-03-27 21:36
测试改名0解析几何几何作图
所属专题 Satz des Pythagoras - Einführung
请求一个直角三角形!在这个任务中，建议使用手表计算器。这个任务适合7-8年级学生，帮助他们检查一个三角形是否是直角三角形，通过反转毕达哥拉斯定理。通过使用GeoGebra，学生可以交互式地探索直角三角形的性质。这个任务使用了GeoGebra的各种命令和对象，包括SelectedIndex、If、Zip、Join等。它适合于学习解析几何和几何构造。

GeoGebra 命令及参数

  1. SelectedIndex(DropDown7) → input7
  2. SelectedIndex(DropDown6) → input6
  3. If(rechtwinkelig, 2, 3) → sol7
  4. If(rechtwinkelig, 2, 3) → sol6
  5. Zip(Text[(("$\textsf{" * m) * "²\vphantom{Öj}}$")], m, listVariables) → listVariablesSquare
  6. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown2
  7. SelectedIndex(DropDown2) → input2
  8. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown1
  9. SelectedIndex(DropDown1) → input1
  10. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown3
  11. SelectedIndex(DropDown3) → input3
  12. SelectedIndex(DropDown0) → input0
  13. Textfield(input4) → Eingabefeld4
  14. Textfield(input5) → Eingabefeld5
  15. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {6, 2, 5, 6, 0, 5, 7, 8, 0, 6, 1, 8, 9, 2, 0, 7, 3, 0, 7, 5, 7, 0, 2, 6, 7, 3, 1, 4, 4, 0, 2, 10, 4, 3, 7, 7, 4, 4, 6, 7, 3, 8, 6, 5, 3, 6, 10, 4, 1, 1, 3, 0, 10, 6, 1, 10, 3, 5, 2, 10, 8, 3, 9, 10, 0, 10, 6, 1, 7, 6, 0, 6, 4, 8, 0, 2, 3, 1, 3, 10, 6, 10, 1, 10, 4, 3, 1, 2, 7, 5, 6, 3, 2, 9, 8, 1, 7, 2, 3, 2}
  16. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  17. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 1, 2, 0, 0, 2, 5, 7, 3, 8, 8, 10, 10, 7, 3, 3, 0, 0, 10, 3, 7, 2, 2, 9, 7, 0, 8, 1, 8, 3, 0, 3, 3, 4, 5, 0, 10, 10, 5, 7, 1, 8, 10, 9, 6, 7, 1, 3, 6, 10, 3, 5, 5, 10, 4, 9, 9, 6, 7, 8, 2, 7, 0, 4, 9, 1, 4, 3, 0, 9, 5, 4, 3, 1, 9, 9, 5, 5, 1, 3, 2, 5, 7, 9, 9, 6, 10, 3, 7, 10, 6, 7, 3, 8, 3, 3, 9, 0, 9, 5}
  18. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  19. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  20. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  21. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  22. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  23. Element({2, 3}, part) → tries
  24. Join(Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, floor(110 / maxexnum)]) → listExnum
  25. Sequence(Sort[listNumsAllABC(m), listNumsABCorder(m)], m, 1, 6) → listNumsAll123
  26. If(startpage ∨ endpage, listPosAll(listPosNum(2)), Pos0) → P2
  27. If(startpage ∨ endpage, listPosAll(listPosNum(3)), Pos0) → P3
  28. If(startpage ∨ endpage, listPosAll(listPosNum(4)), Pos0) → P4
  29. If(startpage ∨ endpage, listPosAll(listPosNum(5)), Pos0) → P5
  30. If(startpage ∨ endpage, listPosAll(listPosNum(6)), Pos0) → P6
  31. If(startpage ∨ endpage, listPosAll(listPosNum(1)), Pos0) → P1
  32. Defined((input4 * input5)) → fixedDropDown6
  33. Text("\textsf\scriptsize{nicht rechtwinklig}", P1 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig1
  34. Text("\textsf\scriptsize{nicht rechtwinklig}", P2 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig2
  35. Text("\textsf\scriptsize{rechtwinklig}", P3 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig3
  36. Text("\textsf\scriptsize{rechtwinklig}", P4 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig4
  37. Text("\textsf\scriptsize{rechtwinklig}", P5 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig5
  38. Text("\textsf\scriptsize{nicht rechtwinklig}", P6 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig6
  39. Rotate(A1 + ((listFactors(1), 0) * listNumsAllABC(1, 3)), 46.5°, A1) → B1
  40. Intersect(Circle[A1, (listNumsAllABC(1, 2) * listFactors(1))], Circle[B1, (listNumsAllABC(1, 1) * listFactors(1))], 1) → C1
  41. Rotate(A2 + ((listFactors(2), 0) * listNumsAllABC(2, 3)), 44°, A2) → B2
  42. Rotate(A3 + ((listFactors(3), 0) * listNumsAllABC(3, 3)), -46.5°, A3) → B3
  43. Rotate(A4 + ((listFactors(4), 0) * listNumsAllABC(4, 3)), 46.5°, A4) → B4
  44. Rotate(A5 + ((listFactors(5), 0) * listNumsAllABC(5, 3)), 46.5°, A5) → B5
  45. Rotate(A6 + ((listFactors(6), 0) * listNumsAllABC(6, 3)), 220°, A6) → B6
  46. Intersect(Circle[A2, (listNumsAllABC(2, 2) * listFactors(2))], Circle[B2, (listNumsAllABC(2, 1) * listFactors(2))], 1) → C2
  47. Intersect(Circle[A3, (listNumsAllABC(3, 2) * listFactors(3))], Circle[B3, (listNumsAllABC(3, 1) * listFactors(3))], 1) → C3
  48. Intersect(Circle[A4, (listNumsAllABC(4, 2) * listFactors(4))], Circle[B4, (listNumsAllABC(4, 1) * listFactors(4))], 1) → C4
  49. Intersect(Circle[A5, (listNumsAllABC(5, 2) * listFactors(5))], Circle[B5, (listNumsAllABC(5, 1) * listFactors(5))], 1) → C5
  50. Intersect(Circle[A6, (listNumsAllABC(6, 2) * listFactors(6))], Circle[B6, (listNumsAllABC(6, 1) * listFactors(6))], 1) → C6
  51. Segment(B1, C1) → a1
  52. Segment(B2, C2) → a2
  53. Segment(B3, C3) → a3
  54. Segment(B4, C4) → a4
  55. Segment(B5, C5) → a5
  56. Segment(B6, C6) → a6
  57. Segment(B1, A1) → c1
  58. Segment(B2, A2) → c2
  59. Segment(B3, A3) → c3
  60. Segment(B4, A4) → c4
  61. Segment(B5, A5) → c5
  62. Segment(B6, A6) → c6
  63. Segment(A1, C1) → b1
  64. Segment(A2, C2) → b2
  65. Segment(A3, C3) → b3
  66. Segment(A4, C4) → b4
  67. Segment(A5, C5) → b5
  68. Segment(A6, C6) → b6
  69. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  70. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  71. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen

AI 绘图提示语参考

绘制一个交互式直角三角形验证工具的界面。屏幕上有6个不同位置的三角形，分别标记为三角形1到三角形6，每个三角形由三个顶点构成。在每个三角形旁边有一个下拉菜单，让用户选择三角形的两条边作为直角边。界面上还有两个输入框用于输入数值，以及多个下拉选择框。当用户选择完毕后，系统会通过文本显示每个三角形是否为直角三角形（“rechtwinklig”）或不是直角三角形（“nicht rechtwinklig”）。整个界面设计用于让学生通过交互操作来验证勾股定理逆定理，检查给定三边长度的三角形是否为直角三角形。
以上提示语为根据原始绘图命令整理而来，仅供参考。