积极 AI Logo 积极 AI

三角形中心与探索

三角形中心与探索
几何画板及绘图内容加载中，请稍等……
2016-04-19 05:40
测试改名0解析几何几何作图
所属专题 Besondere Punkte/Special Points
本范例演示三角形的几何特性，包括重心、垂心、内心和外心等。通过使用GeoGebra命令如Polygon、Midpoint、Line等，可以动态探索三角形的中心点及其性质。适合初中及以上学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(b) → D
  3. Midpoint(a) → E
  4. Midpoint(c) → F
  5. Line(B, D) → d
  6. Line(E, A) → e
  7. Line(C, F) → f
  8. Intersect(d, e) → Centroid
  9. OrthogonalLine(B, b) → g
  10. OrthogonalLine(C, c) → h
  11. OrthogonalLine(A, a) → i
  12. Intersect(g, h) → Orthocentre
  13. AngularBisector(A, B, C) → j
  14. AngularBisector(C, A, B) → k
  15. AngularBisector(B, C, A) → l
  16. Intersect(j, k) → Incentre
  17. LineBisector(c) → m
  18. LineBisector(b) → n
  19. LineBisector(a) → p
  20. Intersect(m, n) → Circumcentre
  21. OrthogonalLine(Incentre, a) → q
  22. Intersect(q, a) → K
  23. Circle(Incentre, K) → r
  24. Circle(Circumcentre, B) → s
  25. Line(Orthocentre, Centroid) → a_1
  26. Circle(Circumcentre, C) → c_1
  27. OrthogonalLine(Incentre, a) → b_1
  28. Intersect(b_1, a) → G
  29. Circle(Incentre, G) → d_1
  30. Line(C, Centroid) → f_1
  31. Intersect(g, b) → H
  32. Angle(C, H, B) → α
  33. Intersect(i, a) → I
  34. Intersect(h, c) → J
  35. Angle(A, J, C) → β
  36. Angle(B, I, Orthocentre) → γ
  37. Angle(A, F, Circumcentre) → δ
  38. Angle(C, D, Circumcentre) → ε
  39. Angle(B, E, Circumcentre) → ζ
  40. Angle(B, C, Incentre) → η
  41. Angle(Incentre, C, A) → θ
  42. Circle(E, D, F) → k_1
  43. Segment(F, E) → m_1
  44. Segment(F, D) → n_1
  45. LineBisector(n_1) → p_1
  46. LineBisector(m_1) → q_1
  47. Intersect(p_1, q_1) → L
  48. Midpoint(Orthocentre, B) → M
  49. Midpoint(Orthocentre, C) → N
  50. Midpoint(Orthocentre, A) → O
  51. Segment(P, A) → r_1
  52. Segment(P, C) → s_1
  53. Segment(P, B) → t_1
  54. Angle(B, P, A) → ι
  55. Angle(A, P, C) → κ
  56. Angle(C, P, B) → λ
  57. LaTeX(μ, true, true) → text4
  58. LaTeX(ι, true, true) → text5
  59. LaTeX(κ, true, true) → text6
  60. LaTeX(λ, true, true) → text7
  61. AngularBisector(c, a) → a_2, b_2
  62. AngularBisector(c, b) → c_2, d_2
  63. AngularBisector(b, a) → e_2, f_2
  64. Intersect(a_2, c_2) → Q
  65. Intersect(c_2, e_2) → R
  66. Intersect(a_2, e_2) → S
  67. OrthogonalLine(Q, c) → g_2
  68. OrthogonalLine(S, a) → h_2
  69. OrthogonalLine(R, b) → i_2
  70. Intersect(g_2, c) → T
  71. Intersect(h_2, a) → U
  72. Intersect(i_2, b) → V
  73. Circle(R, V) → k_2
  74. Circle(Q, T) → p_2
  75. Circle(S, U) → q_2
  76. Line(A, B) → j_2
  77. Line(C, A) → l_2
  78. Line(B, C) → m_2