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中线与重心图解

中线与重心图解
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2019-04-02 23:37
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与重心的关系；②涉及核心数学概念：中线、重心定理、解析几何；③作图要点：使用了中点(Midpoint)、线段(Segment)、交点(Intersect)、缩放(Dilate)、旋转(Rotate)、多边形(Polygon)等GeoGebra命令；④适合高中数学教学或自学，用于理解重心性质。

GeoGebra 命令及参数

  1. Midpoint(A, B) → D
  2. Midpoint(B, C) → E
  3. Midpoint(C, A) → F
  4. Segment(A, B) → a
  5. Segment(B, C) → b
  6. Segment(C, A) → c
  7. Segment(C, D) → d
  8. Segment(A, E) → e
  9. Segment(B, F) → f
  10. Intersect(d, e) → G
  11. Dilate(A, If[0 < g ≤ 1, 1 - g, 0], D) → A'
  12. Segment(A, A') → h
  13. Rotate(A, If[1 < g ≤ 2, ((-(g - 1)) * π), (-π)], D) → A'_1
  14. Rotate(A', If[1 < g ≤ 2, ((g - 1) * π), 3.141592653589793], D) → A''
  15. Segment(A'_1, A'') → h'
  16. Dilate(B, If[2 < g ≤ 3, 3 - g, 0], E) → B'
  17. Segment(B, B') → i
  18. Rotate(B, If[3 < g ≤ 4, ((-(g - 3)) * π), (-π)], E) → B'_1
  19. Rotate(B', If[3 < g ≤ 4, ((g - 3) * π), 3.141592653589793], E) → B''
  20. Segment(B'_1, B'') → i'
  21. Dilate(C, If[4 < g ≤ 5, 5 - g, 0], F) → C'
  22. Segment(C, C') → j
  23. Rotate(C, If[5 < g ≤ 6, ((-(g - 5)) * π), (-π)], F) → C'_1
  24. Rotate(C', If[5 < g ≤ 6, ((g - 5) * π), 3.141592653589793], F) → C''
  25. Segment(C'_1, C'') → j'
  26. Midpoint(G, C) → H
  27. Midpoint(G, B) → I
  28. Midpoint(A, G) → J
  29. Dilate(C, If[6 < g ≤ 7, 7 - g, 0], H) → C'_2
  30. Segment(C, C'_2) → k
  31. Dilate(H, If[7 < g ≤ 8, 8 - g, 0], G) → H'
  32. Segment(H, H') → l
  33. Dilate(G, If[8 < g ≤ 9, 9 - g, 0], D) → G'
  34. Segment(G, G') → m
  35. Dilate(A, If[9 < g ≤ 10, 10 - g, 0], J) → A'_2
  36. Segment(A, A'_2) → n
  37. Dilate(J, If[10 < g ≤ 11, 11 - g, 0], G) → J'
  38. Segment(J, J') → p
  39. Dilate(G, If[11 < g ≤ 12, 12 - g, 0], E) → G'_1
  40. Segment(G, G'_1) → q
  41. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  42. Dilate(F, If[12 < g ≤ 13, 13 - g, 0], G) → F'
  43. Segment(F, F') → r
  44. Rotate(F, If[14 < g ≤ 15, ((g - 14) * π), 3.141592653589793], G) → F'_1
  45. Rotate(F', If[14 < g ≤ 15, ((g - 14) * π), 3.141592653589793], G) → F''
  46. Segment(F'_1, F'') → r'
  47. Rotate(F'_1, If[15 < g ≤ 16, ((g - 15) * π), 3.141592653589793], I) → K
  48. Rotate(F'', If[15 < g ≤ 16, ((g - 15) * π), 3.141592653589793], I) → F'''
  49. Segment(K, F''') → r''
  50. Rotate(G, If[16 < g ≤ 17, ((g - 16) * π), 3.141592653589793], G) → G'_2
  51. Rotate(G'_1, If[16 < g ≤ 17, ((g - 16) * π), 3.141592653589793], G) → L
  52. Segment(G'_2, L) → q'
  53. Rotate(G'_2, If[17 < g ≤ 18, ((g - 17) * π), 3.141592653589793], J) → M
  54. Rotate(L, If[17 < g ≤ 18, ((g - 17) * π), 3.141592653589793], J) → L'
  55. Segment(M, L') → q''
  56. Rotate(G, If[18 < g ≤ 19, ((g - 18) * π), 3.141592653589793], G) → G'_3
  57. Rotate(G', If[18 < g ≤ 19, ((g - 18) * π), 3.141592653589793], G) → G''
  58. Segment(G'_3, G'') → m'
  59. Rotate(G'_3, If[19 < g ≤ 20, ((g - 19) * π), 3.141592653589793], H) → N
  60. Rotate(G'', If[19 < g ≤ 20, ((g - 19) * π), 3.141592653589793], H) → G'''
  61. Segment(N, G''') → m''