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三角形正交中心与中点动态演示

三角形正交中心与中点动态演示
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2017-10-09 08:24
测试改名0几何作图
①本范例动态演示三角形中正交中心与其中一边中点构成的几何现象；②涉及核心概念包括正交中心、三角形中线、旋转、角度、几何变换等；③构造要点运用了 Rotate, Angle, Segment, Ray, Point, Circle, Intersect, CircleSector, Line, OrthogonalLine, Polygon, Midpoint, Dilate 等GeoGebra命令；④适合高中及以上数学学习者用于理解三角形几何性质及动态几何变换。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Circle(B, b) → c
  8. Intersect(c, f, 1) → D
  9. Intersect(c, h, 1) → E
  10. CircleSector(B, D, E) → d
  11. Segment(C, A) → i
  12. Line(C, A) → j
  13. Line(A, B) → k
  14. OrthogonalLine(C, k) → m
  15. Intersect(m, k) → H
  16. Circle(C, 2) → e
  17. Circle(H, 2) → p
  18. Intersect(e, j, 1) → J
  19. Ray(C, J) → n
  20. Line(C, H) → r
  21. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  22. Angle(C, A, B) → β
  23. Midpoint(f) → I
  24. Line(C, B) → l
  25. OrthogonalLine(A, l) → q
  26. Intersect(q, l) → F
  27. Angle(B, F, A) → γ
  28. Intersect(q, r) → G
  29. Segment(C, H) → s
  30. Line(C, H) → t
  31. Circle(C, 2) → d_1
  32. Circle(H, 2) → e_1
  33. Intersect(d_1, t, 1) → L
  34. Intersect(e_1, t) → M, N
  35. Segment(C, H) → h_1
  36. Midpoint(C, G) → O
  37. Circle(B, 1) → k_1
  38. Circle(A, 1) → p_1
  39. Intersect(k_1, k, 2) → P
  40. Intersect(p_1, k, 1) → Q
  41. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], I) → B'
  42. Segment(B, B') → l_1
  43. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], I) → B'_1
  44. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], I) → B''
  45. Segment(B'_1, B'') → m_1
  46. Intersect(k_1, l, 2) → K
  47. Circle(C, 2) → q_1
  48. Intersect(q_1, l, 1) → R
  49. Segment(B, C) → n_1
  50. Ray(C, R) → r_1
  51. Ray(B, K) → s_1
  52. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], F) → A'_1
  53. Segment(A, A'_1) → t_1
  54. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], O) → C'
  55. Segment(C, C') → f_2
  56. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], G) → O'
  57. Segment(O, O') → g_2
  58. Dilate(G, If[5 < o ≤ 6, 6 - o, 0], H) → G'
  59. Rotate(C, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], O) → C'_1
  60. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], O) → C''
  61. Segment(C'_1, C'') → i_2
  62. Dilate(I, If[8 < o ≤ 9, 9 - o, 0], F) → I'
  63. Dilate(O, If[8 < o ≤ 9, 9 - o, 0], F) → O'_1
  64. Line(A, F) → l_2
  65. Line(C, B) → m_2
  66. Line(C, A) → n_2
  67. OrthogonalLine(B, n_2) → p_2
  68. Intersect(n_2, p_2) → S
  69. Dilate(B, If[2 < o ≤ 3, 3 - o, 0], S) → B'_2
  70. Segment(B, B'_2) → q_2
  71. Angle(C, S, B) → ζ
  72. Segment(I, O) → j_2
  73. Line(F, S) → k_2
  74. Intersect(j_2, k_2) → T
  75. Segment(T, O) → g_1
  76. Segment(T, S) → h_2
  77. Segment(T, F) → r_2
  78. Segment(T, I) → s_2
  79. Min({s_2, r_2, h_2, g_1}) → v
  80. Circle(T, (0.5 * v)) → c_2
  81. Intersect(c_2, k_2) → U, V
  82. Dilate(I, If[6 < o ≤ 7, 7 - o, 0], O) → I'_1
  83. Segment(I, I'_1) → t_2
  84. Dilate(F, If[7 < o ≤ 8, 8 - o, 0], T) → F'
  85. Segment(F, F') → a_2
  86. Dilate(T, If[8 < o ≤ 9, 9 - o, 0], S) → T'
  87. Segment(T, T') → b_2
  88. Rotate(U, If[9 < o ≤ 10, ((o - 9) * π / 2), π / 2], T) → U'
  89. CircleSector(T, U, U') → d_2
  90. Rotate(d_2, If[11 < o ≤ 12, ((o - 11) * π / 2), π / 2], T) → e_2