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三角形的四个基本中心

三角形的四个基本中心
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2014-04-13 05:24
测试改名0圆角向量几何作图
这个范例演示了三角形的四个基本中心（重心、外心、内心、垂心），以及它们之间的关系，并展示了中位线。通过 GeoGebra 命令如 Segment（线段）、AngularBisector（角平分线）、Line（直线）、OrthogonalLine（垂线）、LineBisector（中垂线）、Intersect（交点）、Circle（圆）、Angle（角度）等，构建了点、边、角平分线、高、中垂线、外接圆、内切圆等对象，适合高中数学教学和几何作图学习。

GeoGebra 命令及参数

  1. Segment(PointC, PointB) → SideA
  2. Segment(PointA, PointC) → SideB
  3. Segment(PointB, PointA) → SideC
  4. AngularBisector(PointA, PointC, PointB) → AngleBisLineB2
  5. Line(PointC, PointB) → LineA
  6. OrthogonalLine(PointA, LineA) → AltitudeB1
  7. Line(PointA, PointC) → LineB
  8. OrthogonalLine(PointB, LineB) → AltitudeB3
  9. Line(PointB, PointA) → LineC
  10. OrthogonalLine(PointC, LineC) → AltitudeB2
  11. LineBisector(SideC) → PerpBisB1
  12. LineBisector(SideB) → PerpBisB3
  13. LineBisector(SideA) → PerpBisB2
  14. Intersect(PerpBisB1, PerpBisB2) → Circumcenter
  15. Segment(Circumcenter, PointC) → Circum1
  16. Segment(Circumcenter, PointA) → Circum2
  17. Segment(Circumcenter, PointB) → Circum3
  18. Circle(Circumcenter, Circum1) → Circumcircle
  19. Intersect(PerpBisB2, SideA) → Midpoint1
  20. Intersect(PerpBisB1, SideC) → Midpoint2
  21. Intersect(PerpBisB3, SideB) → Midpoint3
  22. Segment(Circumcenter, Midpoint3) → PerpBis1
  23. Segment(Circumcenter, Midpoint1) → PerpBis2
  24. Segment(Circumcenter, Midpoint2) → PerpBis3
  25. AngularBisector(PointB, PointA, PointC) → AngleBisLineB1
  26. AngularBisector(PointC, PointB, PointA) → AngleBisLineB3
  27. Intersect(AngleBisLineB1, AngleBisLineB2) → IncenterLine
  28. OrthogonalLine(IncenterLine, LineC) → IncenterB1
  29. OrthogonalLine(IncenterLine, LineA) → IncenterB2
  30. OrthogonalLine(IncenterLine, LineB) → IncenterB3
  31. Intersect(IncenterB1, SideC) → IncenterA1
  32. Intersect(IncenterB3, SideB) → IncenterA2
  33. Intersect(IncenterB2, SideA) → IncenterA3
  34. Intersect(AngleBisLineB1, SideA) → AngBisA1
  35. Intersect(AngleBisLineB3, SideB) → AngBisA2
  36. Segment(AngBisA1, PointA) → AngBisect1
  37. Intersect(AngleBisLineB2, SideC) → AngBisA3
  38. Segment(AngBisA3, PointC) → AngBisect2
  39. Segment(AngBisA2, PointB) → AngBisect3
  40. Segment(IncenterLine, IncenterA1) → Incenter1
  41. Segment(IncenterLine, IncenterA3) → Incenter2
  42. Segment(IncenterLine, IncenterA2) → Incenter3
  43. Intersect(AngBisect1, AngBisect2) → Incenter
  44. Circle(Incenter, Incenter1) → Incircle
  45. Angle(Incenter, IncenterA2, PointA) → IncenterA
  46. Angle(Incenter, IncenterA1, PointB) → IncenterB
  47. Angle(Incenter, IncenterA3, PointC) → IncenterC
  48. Segment(PointB, Midpoint3) → Median1
  49. Segment(Midpoint2, PointC) → Median2
  50. Segment(PointA, Midpoint1) → Median3
  51. Intersect(Median1, Median2) → Centroid
  52. Intersect(AltitudeB1, AltitudeB2) → Orthocenter
  53. Intersect(AltitudeB2, LineC) → AltitudeA1
  54. Angle(Orthocenter, AltitudeA1, PointB) → AltitudeA
  55. Intersect(AltitudeB1, LineA) → AltitudeA3
  56. Angle(Orthocenter, AltitudeA3, PointC) → AltitudeB
  57. Intersect(AltitudeB3, LineB) → AltitudeA2
  58. Angle(Orthocenter, AltitudeA2, PointA) → AltitudeC
  59. Segment(PointC, AltitudeA1) → Altitude1
  60. Segment(PointA, AltitudeA3) → Altitude2
  61. Segment(PointB, AltitudeA2) → Altitude3
  62. Angle(Circumcenter, Midpoint2, PointB) → PerpBisA
  63. Angle(Circumcenter, Midpoint1, PointC) → PerpBisB
  64. Angle(Circumcenter, Midpoint3, PointA) → PerpBisC
  65. Segment(Midpoint2, PointA) → MidpointC1
  66. Segment(Midpoint2, PointB) → MidpointC2
  67. Segment(PointB, Midpoint1) → MidpointA1
  68. Segment(Midpoint1, PointC) → MidpointA2
  69. Segment(PointC, Midpoint3) → MidpointB1
  70. Segment(Midpoint3, PointA) → MidpointB2
  71. Angle(AngBisA3, PointB, AngBisA2) → AngleBisA1
  72. Angle(AngBisA2, PointB, PointC) → AngleBisA2
  73. Angle(PointC, PointA, AngBisA1) → AngleBisB1
  74. Angle(AngBisA1, PointA, PointB) → AngleBisB2
  75. Angle(PointB, PointC, AngBisA3) → AngleBisC1
  76. Angle(AngBisA3, PointC, PointA) → AngleBisC2
  77. Segment(Midpoint2, Midpoint1) → MidB
  78. Segment(Midpoint1, Midpoint3) → MidC
  79. Segment(Midpoint3, Midpoint2) → MidA
  80. OrthogonalLine(PointA, LineA) → AltLineA
  81. OrthogonalLine(PointC, LineC) → AltLineC
  82. OrthogonalLine(PointB, LineB) → AltLineB
  83. Line(Circumcenter, Orthocenter) → EulerLine
  84. Angle(PointA, PointC, PointB) → VertC
  85. Angle(PointC, PointB, PointA) → VertA
  86. Angle(PointB, PointA, PointC) → VertB

AI 绘图提示语参考

画一个三角形，并分别作出它的三条边的中垂线，交点为外心，连接外心与三个顶点得到外接圆。接着，作出三角形的三条角平分线，交点为内心，连接内心与三边交点得到内切圆。再作出三角形的三条高，交点为垂心。最后，连接各边中点得到中位线，展示这些中心与线段的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。