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中线、重心、高线与垂心

中线、重心、高线与垂心
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2016-12-01 00:08
测试改名0解析几何几何作图
①本范例演示了三角形中线、重心、高线与垂心的关系与性质；②涉及核心数学概念包括中线、重心、高线、垂心、三角形几何性质；③作图要点：使用Polygon命令绘制三角形，Angle命令测量角度，Circle命令画圆，Intersect命令求交点，Line和Segment命令画线段，Distance和Midpoint命令计算距离和中点；④适合高中数学教学与学习，用于理解三角形的重要几何元素及其相互关系。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(B, A, C) → α
  3. Angle(A, C, B) → β
  4. Angle(C, B, A) → γ
  5. Circle(A, B) → d
  6. Circle(B, A) → e
  7. Intersect(d, e, 2) → D
  8. Intersect(d, e, 1) → E
  9. Line(D, E) → f
  10. Circle(A, C) → g
  11. Circle(C, A) → h
  12. Intersect(g, h, 2) → F
  13. Intersect(g, h, 1) → G
  14. Line(F, G) → i
  15. Circle(C, B) → k
  16. Circle(B, C) → p
  17. Intersect(k, p, 2) → H
  18. Intersect(k, p, 1) → I
  19. Line(H, I) → j
  20. Intersect(f, c) → J
  21. Intersect(i, b) → K
  22. Intersect(j, a) → L
  23. Segment(A, L) → l
  24. Segment(B, K) → m
  25. Segment(J, C) → n
  26. Intersect(l, m) → M
  27. Circle(A, B) → q
  28. Circle(C, B) → r
  29. Intersect(q, r, 2) → N
  30. Line(B, N) → s
  31. Intersect(s, b) → O
  32. Circle(B, A) → t
  33. Circle(C, A) → c_1
  34. Intersect(t, c_1, 2) → P
  35. Line(A, P) → f_1
  36. Intersect(f_1, a) → Q
  37. Segment(B, O) → g_1
  38. Segment(A, Q) → h_1
  39. Circle(A, B) → d_1
  40. Circle(B, C) → e_1
  41. Intersect(d_1, e_1, 2) → R
  42. Line(R, C) → i_1
  43. Intersect(i_1, c) → S
  44. Segment(C, S) → j_1
  45. Angle(N, O, A) → δ
  46. Angle(A, Q, B) → ε
  47. Circle(A, C) → k_1
  48. Circle(B, C) → p_1
  49. Intersect(k_1, p_1, 2) → T
  50. Line(T, C) → l_1
  51. Intersect(l_1, c) → U
  52. Angle(A, U, T) → ζ
  53. Segment(U, C) → m_1
  54. Intersect(s, f_1) → V
  55. Distance(A, M) → AM
  56. Distance(A, M) → distanceAM
  57. Distance(C, M) → distanceCM
  58. Distance(B, A) → distanceBA
  59. Distance(L, A) → distanceLA
  60. Distance(M, l) → distanceMl
  61. Distance(L, M) → distanceLM
  62. Distance(C, J) → distanceCJ
  63. Distance(M, J) → distanceMJ
  64. Distance(B, K) → distanceBK
  65. Distance(B, M) → distanceBM
  66. Distance(B, K) → o
  67. Midpoint(B, K) →
  68. Distance(B, M) → u
  69. Midpoint(B, M) →
  70. Distance(B, K) → v
  71. Midpoint(B, K) →
  72. Distance(M, K) → distanceMK
  73. Midpoint(M, K) →
  74. Distance(B, M) → w
  75. Midpoint(B, M) →
  76. Distance(M, K) → a_1
  77. Midpoint(M, K) →
  78. Distance(B, K) → b_1
  79. Midpoint(B, K) →
  80. Distance(L, A) → n_1
  81. Midpoint(L, A) →
  82. Distance(A, M) → o_1
  83. Midpoint(A, M) →
  84. Distance(L, M) → q_1
  85. Midpoint(L, M) →

AI 绘图提示语参考

绘制一个三角形，并标出三个内角。分别以每两个顶点为圆心、以对应边长为半径作圆，利用两圆交点作出每条边的垂直平分线，从而找到各边中点。连接每个顶点与对边中点，画出三条中线，它们交于重心。接着，分别以每两个顶点为圆心、以对应边长为半径作圆，利用交点作出每条边的高线，三条高线交于垂心。最后，标出重心和垂心，并显示相关角度。
以上提示语为根据原始绘图命令整理而来，仅供参考。