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平行角配对：平行线条件判断

平行角配对：平行线条件判断
几何画板及绘图内容加载中，请稍等……
2024-03-26 17:49
角数列几何作图
所属专题 Besondere Winkelpaare
本例通过多项选择与开放性练习，引导学生探索平行线条下的角对关系，包括平行角、补充角及其大小比较。练习涵盖角的分类、测量及性质描述，要求学生在图形中识别并标记平行直线的射线，理解补充平行角的性质。构造摘要中涉及的GeoGebra命令包括Sequence、Element、If、Segment、Angle及SelectedIndex等，通过这些交互式组件实现问题的生成、答案验证及几何图形的动态展示，适合初中（五、六年级）几何教学与角度性质巩固。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 1, 2, 2, 9, 7, 3, 4, 4, 7}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. If(step ≟ 1, sbheight01, sbheight06, step ≟ 2, sbheight02, step ≟ 3, sbheight03, step ≟ 4, sbheight04, step ≟ 5, sbheight05) → sbheight
  5. If(step ≟ 1, sbwidth01, sbwidth06, step ≟ 2, sbwidth02, step ≟ 3, sbwidth03, step ≟ 4, sbwidth04, step ≟ 5, sbwidth05) → sbwidth
  6. SpeechBubbleLeft(PosSB01 + (0, If[step ≟ 2, 0, 0]), sbwidth, sbheight) → poly1
  7. Segment(Pos11, Pos12) → seg12
  8. Segment(Pos11, Pos13) → seg13
  9. Segment(Pos21, Pos22) → seg22
  10. Segment(Pos21, Pos23) → seg23
  11. Angle(Pos13, Pos11, Pos12) → alpha1
  12. Angle(Pos23, Pos21, Pos22) → alpha2
  13. SelectedIndex(dropdown21) → index21
  14. Sequence(Pos11 + (3.75 * (cos((1° * k)), sin((1° * k)))), k, 1, 360) → PosList4
  15. Point(PosList4) → Pos41
  16. Point(PosList4) → Pos42
  17. Segment(Pos11, Pos11 + (4 * UnitVector[Vector[Pos11, Pos41]])) → seg41
  18. Segment(Pos11, Pos11 + (4 * UnitVector[Vector[Pos11, Pos42]])) → seg42
  19. IndexOf(Pos41, PosList4) → index41
  20. IndexOf(Pos42, PosList4) → index42
  21. Segment(Pos21, Pos21 + (4 * UnitVector[Vector[Pos21, Pos43]])) → seg43
  22. Segment(Pos21, Pos21 + (4 * UnitVector[Vector[Pos21, Pos44]])) → seg44
  23. Angle(Pos11 + (4 * UnitVector[Vector[Pos11, Pos41]]), Pos11, Pos11 + (4 * UnitVector[Vector[Pos11, Pos42]])) → alpha41
  24. Angle(Pos21 + (4 * UnitVector[Vector[Pos21, Pos43]]), Pos21, Pos21 + (4 * UnitVector[Vector[Pos21, Pos44]])) → alpha42
  25. SelectedIndex(dropdown41) → indexdd41
  26. Segment(Pos51, Pos52) → seg52
  27. Segment(Pos51, Pos53) → seg53
  28. Segment(Pos54, Pos55) → seg55
  29. Segment(Pos54, Pos56) → seg56
  30. Angle(Pos52, Pos51, Pos53) → beta1
  31. Angle(Pos55, Pos54, Pos56) → beta2
  32. Sequence(Pos51 + (3.75 * (cos((1° * k)), sin((1° * k)))), k, 1, 360) → PosList5
  33. Point(PosList5) → Pos61
  34. Point(PosList5) → Pos62
  35. IndexOf(Pos61, PosList5) → index61
  36. IndexOf(Pos62, PosList5) → index62
  37. Segment(Pos54, Pos63) → seg63
  38. Segment(Pos54, Pos64) → seg64
  39. Segment(Pos51, Pos51 + (4 * UnitVector[Vector[Pos51, Pos61]])) → seg61
  40. Segment(Pos51, Pos51 + (4 * UnitVector[Vector[Pos51, Pos62]])) → seg62
  41. Angle(Pos51 + (4 * UnitVector[Vector[Pos51, Pos61]]), Pos51, Pos51 + (4 * UnitVector[Vector[Pos51, Pos62]])) → beta61
  42. Angle(Pos54 + (4 * UnitVector[Vector[Pos54, Pos63]]), Pos54, Pos54 + (4 * UnitVector[Vector[Pos54, Pos64]])) → beta62
  43. Textfield(input61) → InputBox61
  44. Angle(seg71(1), seg71(2)) → alpha71
  45. Angle(seg72(1), seg72(2)) → alpha72
  46. Angle(seg73(1), seg73(2)) → beta71
  47. Angle(seg74(1), seg74(2)) → beta72
  48. If(step ≟ 2, correctdd21 ∧ selectedseg, step ≟ 4, moved4 ∧ correctdd41, step ≟ 6, moved6 ∧ correct61, true) → clickableBtnNext
  49. Segment(Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle))), Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[Pos11, Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow412
  50. Segment(Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle))), Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[Pos11, Pos11 + (Distance[Pos11, Pos41] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos41] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow411
  51. Segment(Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle))), Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[Pos11, Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow421
  52. Segment(Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle))), Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[Pos11, Pos11 + (Distance[Pos11, Pos42] * (cos(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos11 + (1, 0), Pos11, Pos42] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow422
  53. Segment(Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle))), Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[Pos51, Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow611
  54. Segment(Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle))), Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[Pos51, Pos51 + (Distance[Pos51, Pos61] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos61] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow612
  55. Segment(Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle))), Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[Pos51, Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow621
  56. Segment(Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle))), Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[Pos51, Pos51 + (Distance[Pos51, Pos62] * (cos(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle), sin(Angle[Pos51 + (1, 0), Pos51, Pos62] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow622

AI 绘图提示语参考

绘制两条平行线，分别标记为线段12和线段22。在每条线上选择一个点，从该点画两条平行线段，长度为4个单位。在每条线段上选择一个点，从该点画两条射线，形成角度alpha1和alpha2。在两条平行线之间画两条线段，形成角度beta1和beta2。根据给定的角度值，调整射线的位置，使角度alpha41和alpha42分别等于给定的角度值。最后，根据角度关系，调整线段的位置，使角度beta61和beta62分别等于给定的角度值。
以上提示语为根据原始绘图命令整理而来，仅供参考。