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共点线演示

共点线演示
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2019-01-10 09:14
测试改名0几何作图
①本范例演示了三角形中三条中线、角平分线、高线的交点（重心、外心、内心）的共点性；②涉及核心概念：重心、外心、内心、角平分线、中线、高线、三角形几何性质；③作图要点：使用Polygon、Angle、LineBisector、Intersect、Segment、AngularBisector、OrthogonalLine、Midpoint、Line等命令构造三角形及各特殊点与线；④适合高中数学教学和学生几何性质探究。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → t1, c, a, b
  2. Angle(B, A, C) → α
  3. Angle(A, B, C) → β
  4. Angle(A, C, B) → γ
  5. LineBisector(c) → f
  6. LineBisector(a) → g
  7. LineBisector(b) → h
  8. Intersect(g, a) → D
  9. Intersect(h, b) → E
  10. Intersect(f, c) → F
  11. Intersect(f, g) → Circumcenter
  12. Segment(Circumcenter, F) → i
  13. Segment(Circumcenter, D) → j
  14. Segment(Circumcenter, E) → k
  15. AngularBisector(B, A, C) → l
  16. AngularBisector(B, C, A) → m
  17. AngularBisector(A, B, C) → n
  18. Intersect(l, m) → Incenter
  19. Segment(A, Incenter) → p
  20. Segment(B, Incenter) → q
  21. Segment(C, Incenter) → r
  22. Segment(Circumcenter, B) → s
  23. Segment(Circumcenter, C) → t
  24. Segment(Circumcenter, A) → f_1
  25. OrthogonalLine(Incenter, b) → g_1
  26. OrthogonalLine(Incenter, c) → h_1
  27. OrthogonalLine(Incenter, a) → i_1
  28. Intersect(i_1, a) → I
  29. Intersect(g_1, b) → J
  30. Intersect(h_1, c) → K
  31. Segment(Incenter, K) → j_1
  32. Segment(Incenter, I) → k_1
  33. Segment(Incenter, J) → l_1
  34. Midpoint(a) → L
  35. Midpoint(b) → M
  36. Midpoint(c) → N
  37. Segment(A, L) → m_1
  38. Segment(B, M) → n_1
  39. Segment(C, N) → p_1
  40. Intersect(m_1, n_1) → Centroid
  41. Segment(A, Centroid) → q_1
  42. Segment(Centroid, L) → r_1
  43. Segment(N, Centroid) → s_1
  44. Segment(Centroid, C) → t_1
  45. Segment(M, Centroid) → a_1
  46. Segment(Centroid, B) → b_1
  47. OrthogonalLine(C, c) → c_1
  48. OrthogonalLine(A, a) → d_1
  49. OrthogonalLine(B, b) → e_1
  50. Line(A, C) → i_2
  51. Line(C, B) → j_2
  52. Line(A, B) → k_2
  53. OrthogonalLine(A, j_2) → f_2
  54. OrthogonalLine(B, i_2) → g_2
  55. OrthogonalLine(C, k_2) → h_2
  56. Intersect(f_2, g_2) → Orthocenter
  57. Intersect(k_2, h_2) → Q
  58. Intersect(j_2, f_2) → R
  59. Intersect(i_2, g_2) → S
  60. Segment(B, S) → l_2
  61. Segment(C, Q) → m_2
  62. Segment(A, R) → n_2
  63. Segment(Orthocenter, Q) → p_2
  64. Segment(Orthocenter, R) → q_2
  65. Segment(Orthocenter, S) → r_2