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补角与邻角

补角与邻角
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2024-02-13 21:29
角变换几何作图滑块动画
所属专题 Besondere Winkelpaare
①本范例演示了补角与邻角的几何关系；②涉及的核心数学概念包括补角的定义（两角和为180°）、邻角的定义（共顶点且一边重合）以及角度大小的比较；③作图要点——从下方『构造摘要』提炼用到了GeoGebra命令/对象：SpeechBubbleLeft, Circle, Point, Segment, OrthogonalLine, Intersect, Mirror, Arc, Angle, Vector, Rotate, Translate, SelectedIndex, CircleArc, Textfield；④适合小学5-6年级学生，用于学习和理解角度分类及补角、邻角的概念。

GeoGebra 命令及参数

  1. SpeechBubbleLeft(PBubble - (0, 1), 12.4, 2.9) → poly1
  2. SpeechBubbleLeft(PBubble + (0, 0.55), 11, 1.3) → poly2
  3. SpeechBubbleLeft(PBubble, 5, 1) → poly3
  4. Circle(A, 3.4) → c
  5. Point(c) → B
  6. Segment(A, B) → s11
  7. OrthogonalLine(A, s11) → perpLine
  8. Intersect(c, perpLine, 2) → MCOM
  9. Mirror(B, A) → MSUP
  10. Arc(c, B, MSUP) → supplArc
  11. Point(supplArc) → B'
  12. Angle(B, A, B') → α
  13. Segment(A, B') → s12
  14. Circle(A, 2.3) → cExt
  15. Mirror(B, cExt) → B'_{2}
  16. Segment(B, B'_{2}) → sv11
  17. Mirror(B', cExt) → B''_{1}
  18. Segment(B', B''_{1}) → sv12
  19. Vector(C, V) → u
  20. Rotate(D, 180° - α, C) → D'
  21. Segment(C, D) → s21
  22. Segment(C, D') → s22
  23. Vector(A, V) → v
  24. Translate(A, Vector[(transSli1 * v)]) → A'
  25. Translate(D', Vector[(transSli2 * u)]) → D''
  26. Translate(B, Vector[(transSli1 * v)]) → B'_{1}
  27. Angle(D'', V, B'_{1}) → ang
  28. Rotate(A', (rotAng * rotSli), V) → A''
  29. Translate(A, Vector[(transSli1 * v)]) → A'_{1}
  30. Translate(B', Vector[(transSli1 * v)]) → B''
  31. Rotate(B'', (rotAng * rotSli), V) → B'''
  32. Translate(B', Vector[(transSli1 * u)]) → B''_{2}
  33. Translate(B', Vector[(transSli1 * v)]) → B''_{3}
  34. Translate(B, Vector[(transSli1 * u)]) → B'_{3}
  35. Translate(B, Vector[(transSli1 * v)]) → B'_4
  36. Rotate(B, α - 15°, A) → BF
  37. Translate(C, u) → C'
  38. Translate(C, u) → C'_{1}
  39. Translate(C, Vector[(transSli2 * u)]) → C'_{2}
  40. Translate(C, Vector[(transSli2 * u)]) → C'_{3}
  41. Translate(D, Vector[(transSli2 * u)]) → D'_{1}
  42. Point(s11) → E
  43. Point(s21) → F
  44. Rotate(A'_{1}, (rotAng * rotSli), V) → G
  45. Rotate(B'_{1}, (rotAng * rotSli), V) → H
  46. Rotate(B'_4, (rotAng * rotSli), V) → S
  47. Rotate(B''_{3}, (rotAng * rotSli), V) → T
  48. Segment(G, H) → s11''
  49. Segment(A'', B''') → s12''
  50. Segment(C'_{2}, D'_{1}) → s21'
  51. Segment(C'_{3}, D'') → s22'
  52. Angle(D'_{1}, C'_{2}, D'') → β
  53. Angle(H, A', B''') → α'
  54. Angle(D'_{1} + (2, 0), A', B''' - (2, 0)) → γ
  55. SelectedIndex(dropdown) → index
  56. CircleArc(A', D'_{1} - (0.4, 0), B''') → d
  57. Point(d) → arrowCirclePoint
  58. Segment(A', arrowCirclePoint) → seg
  59. CircleArc(A', D'_{1} - (0.23, 0), B''') → e
  60. Mirror(arrowCirclePoint, e) → I'
  61. Segment(arrowCirclePoint, I') → seg2
  62. Angle(I', A', B''') → α''
  63. Angle(D'_{1}, A', I') → β'
  64. SpeechBubbleLeft(PBubble, 12.4, 1.9) → poly1_1
  65. Textfield(input1) → InputBox1
  66. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle)))]])) → f
  67. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle)))]])) → g

AI 绘图提示语参考

画一个包含补角和邻角关系的几何图：先画一个大圆，在圆上取一点作为顶点，从该顶点向圆上另一点作线段，再过顶点作该线段的垂线，与圆相交得到另一个点。以顶点为中心，将圆上的第二个点镜像到对称位置，形成补角关系，画出这两点间的圆弧并标记角度。在大圆内部再画一个小同心圆，将大圆上的点关于小圆做镜像，得到若干对应点。用向量将某些点进行平移，再用旋转功能对部分点进行旋转，最后将相关点用线段连接，展示补角和邻角的各种位置关系。图中用多个语音气泡标注角度信息和说明文字。
以上提示语为根据原始绘图命令整理而来，仅供参考。