三角形中线演示

三角形中线演示
几何画板及绘图内容加载中,请稍等……
2015-01-01 02:04
①本范例演示了三角形中线的性质与构造;②涉及的核心数学概念包括三角形中线、重心、角平分线、垂线等;③作图要点提炼自构造摘要,使用了Polygon、midtri、Line、Angle、Intersect、Distance、OrthogonalLine、Segment、Midpoint、Circle、AngularBisector等GeoGebra命令/对象;④适合高中数学教学或几何爱好者学习使用。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(D, E, F) → poly2, f, d, e
  3. midtri(F, D, E) → G, H, I, poly3
  4. midtri(I, G, H) → J, K, L, poly4
  5. midtri(K, L, J) → M, N, O, poly5
  6. midtri(N, O, M) → P, Q, R, poly6
  7. Line(A, H) → i
  8. Line(B, I) → j
  9. Line(C, G) → k
  10. Angle(F, A, E) → α
  11. Angle(C, B, A) → β
  12. Angle(A, C, B) → γ
  13. Angle(E, D, F) → δ
  14. Angle(F, E, D) → ε
  15. Angle(D, F, E) → ζ
  16. Angle(C, D, E) → η
  17. Angle(D, E, C) → θ
  18. Angle(E, F, A) → ι
  19. Angle(A, E, F) → κ
  20. Angle(B, F, D) → λ
  21. Angle(F, D, B) → μ
  22. Line(S, A) → m
  23. Line(S, C) → n
  24. Line(S, B) → p
  25. Intersect(p, b) → T
  26. Distance(A, T) → distanceAT
  27. Distance(T, C) → distanceTC
  28. Intersect(m, a) → U
  29. Intersect(n, c) → V
  30. Distance(A, V) → distanceAV
  31. Distance(V, B) → distanceVB
  32. Distance(B, U) → distanceBU
  33. Distance(U, C) → distanceUC
  34. OrthogonalLine(S, b) → q
  35. OrthogonalLine(S, c) → r
  36. OrthogonalLine(S, a) → s
  37. Intersect(s, a) → W
  38. Intersect(q, b) → Z
  39. Intersect(r, c) → A_1
  40. Segment(A_1, S) → t
  41. Segment(W, S) → a_1
  42. Segment(Z, S) → b_1
  43. Angle(S, A_1, A) → ν
  44. Angle(C, W, S) → ξ
  45. Angle(A, Z, S) → ο
  46. Midpoint(a) → B_1
  47. Midpoint(c) → C_1
  48. Midpoint(b) → D_1
  49. OrthogonalLine(C_1, c) → c_1
  50. OrthogonalLine(D_1, b) → d_1
  51. OrthogonalLine(B_1, a) → e_1
  52. Intersect(c_1, d_1) → E_1
  53. Segment(E_1, B) → f_1
  54. Segment(E_1, A) → g_1
  55. Segment(E_1, C) → h_1
  56. Circle(E_1, B) → k_1
  57. AngularBisector(C, B, A) → i_1
  58. AngularBisector(B, A, C) → j_1
  59. AngularBisector(A, C, B) → l_1
  60. Intersect(i_1, j_1) → F_1
  61. Angle(F_1, C, B) → ρ
  62. Angle(A, C, F_1) → σ

AI 绘图提示语参考

画一个三角形,并展示其三条中位线。在中位线上找到中点,并连接这些中点形成一个新的三角形。标注原三角形的顶点和中位线的中点,并画出从顶点到中位线的线段。测量并显示这些线段的长度,以及新三角形与原三角形的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。