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三角形中的特殊线段与点

三角形中的特殊线段与点
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2016-02-22 21:28
测试改名0圆几何作图
①本范例演示了三角形中的特殊线段（如角平分线、中线、高线）与特殊点（如内心、外心、重心、垂心）的几何性质与相互关系；②涉及核心数学概念包括角平分线定理、中线性质、垂心与重心坐标、三角形内心与外心关系；③作图要点提炼自GeoGebra命令：Polygon构建三角形，LineBisector作角平分线，Intersect求交点，AngularBisector作角平分线，Segment画线段，Circle画圆，OrthogonalLine作垂线，Angle测量角度；④适合高中数学几何作图教学与探究性学习，可用于理解三角形中心与特殊线段的性质与联系。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(c) → pbc
  3. LineBisector(a) → pba
  4. LineBisector(b) → pbb
  5. Intersect(pbc, pba) → CC
  6. AngularBisector(B, A, C) → aba
  7. AngularBisector(A, C, B) → abc
  8. AngularBisector(A, B, C) → abb
  9. Intersect(aba, abc) → CI
  10. Intersect(pba, a) → MA
  11. Intersect(pbb, b) → MB
  12. Intersect(pbc, c) → MC
  13. Segment(A, MA) → ma
  14. Segment(B, MB) → mb
  15. Segment(C, MC) → mc
  16. Intersect(ma, mb) → CG
  17. Circle(CC, B) → cc
  18. OrthogonalLine(CI, a) → auxlineperp
  19. Intersect(auxlineperp, a) → AUXpoint
  20. Circle(CI, AUXpoint) → ci
  21. Angle(C, MA, CC) → α
  22. Angle(B, MC, CC) → β
  23. Angle(A, MB, CC) → γ
  24. Angle(C, B, CI) → δ
  25. Angle(CI, B, A) → ε
  26. Angle(B, A, CI) → ζ
  27. Angle(CI, A, C) → η
  28. Angle(A, C, CI) → θ
  29. Angle(CI, C, B) → ι
  30. Segment(C, MA) → a1
  31. Segment(MA, B) → a2
  32. Segment(A, MB) → b1
  33. Segment(MB, C) → b2
  34. Segment(B, MC) → c1
  35. Segment(MC, A) → c2
  36. Angle(B, MC, SC) → κ
  37. Angle(A, MB, SB) → λ
  38. Angle(C, MA, SA) → μ
  39. OrthogonalLine(A, a) → hlineA
  40. OrthogonalLine(B, b) → hlineB
  41. OrthogonalLine(C, c) → hlineC
  42. Intersect(hlineA, Line[B, C]) → fA
  43. Intersect(hlineB, Line[A, C]) → fB
  44. Intersect(hlineC, Line[A, B]) → fC
  45. Intersect(hlineA, hlineB) → ORT
  46. Segment(fA, B) → fAB
  47. Segment(fA, C) → fAC
  48. Segment(fB, A) → fBA
  49. Segment(fB, C) → fBC
  50. Segment(fC, A) → fCA
  51. Segment(fC, B) → fCB
  52. Intersect(fCB, fAB) → E
  53. Segment(A, fA) → hA
  54. Segment(B, fB) → hB
  55. Segment(C, fC) → hC
  56. Segment(fA, ORT) → auxhA
  57. Segment(fB, ORT) → auxhB
  58. Segment(fC, ORT) → auxhC
  59. Angle(C, fA, A) → angfA1
  60. Angle(B, fC, C) → angfC1
  61. Angle(A, fB, B) → angfB1
  62. Angle(A, fA, C) → angfA2
  63. Angle(B, fB, A) → angfB2
  64. Angle(C, fC, B) → angfC2
  65. Polygon(Corner[1], Corner[2], Corner[3], Corner[4]) → poly2, d, e, f, g