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三角形反射与对称变换演示

三角形反射与对称变换演示
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2016-08-31 11:56
测试改名0角向量变换几何作图
该范例通过GeoGebra动态展示一个三角形关于某条直线（或轴）进行反射（镜像）后，得到其对称像的过程，并同时呈现多个相关几何对象（如反射后的三角形、辅助线段、角度、统计特征等）的联动变化。核心数学概念包括平面几何中的反射变换、轴对称、对称性、向量（二维向量）以及单位圆上的角度关系。作图要点：使用Polygon命令构造原始三角形（顶点A、B、C），利用Mirror命令生成反射后的三角形（顶点A2、B2、C2等），并通过Segment、Angle、TableText等命令绘制辅助线段、标注角度和生成数据表格；同时涉及SD（标准差）等统计特征，可能用于分析反射前后图形的几何量。该范例适合初中至高中阶段的学生学习几何变换、对称性质以及动态数学软件的操作，也可用于教师课堂演示，帮助学生直观理解反射变换对图形位置、形状和度量属性的影响。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → D2, E2, F2, G2
  2. Mirror(A2, F2) → A3
  3. Mirror(B2, G2) → B3
  4. Mirror(C2, E2) → C3
  5. Polygon(A3, B3, C3) → D3, E3, F3, G3
  6. Mirror(A3, F3) → A4
  7. Mirror(B3, G3) → B4
  8. Mirror(C3, E3) → C4
  9. Polygon(A4, B4, C4) → D4, E4, F4, G4
  10. Mirror(A4, F4) → A5
  11. Mirror(B4, G4) → B5
  12. Mirror(C4, E4) → C5
  13. Polygon(A5, B5, C5) → D5, E5, F5, G5
  14. Mirror(A5, F5) → A6
  15. Mirror(B5, G5) → B6
  16. Mirror(C5, E5) → C6
  17. Polygon(A6, B6, C6) → D6, E6, F6, G6
  18. Mirror(A6, F6) → A7
  19. Mirror(B6, G6) → B7
  20. Mirror(C6, E6) → C7
  21. Polygon(A7, B7, C7) → D7, E7, F7, G7
  22. Mirror(A7, F7) → A8
  23. Mirror(B7, G7) → B8
  24. Mirror(C7, E7) → C8
  25. Polygon(A8, B8, C8) → D8, E8, F8, G8
  26. Mirror(A8, F8) → A9
  27. Mirror(B8, G8) → B9
  28. Mirror(C8, E8) → C9
  29. Polygon(A9, B9, C9) → D9, E9, F9, G9
  30. Mirror(A9, F9) → A10
  31. Mirror(B9, G9) → B10
  32. Mirror(C9, E9) → C10
  33. Polygon(A10, B10, C10) → D10, E10, F10, G10
  34. Mirror(A10, F10) → A11
  35. Mirror(B10, G10) → B11
  36. Mirror(C10, E10) → C11
  37. Polygon(A11, B11, C11) → D11, E11, F11, G11
  38. SD({E2, F2, G2}) → J2
  39. SD({E3, F3, G3}) → J3
  40. SD({E4, F4, G4}) → J4
  41. SD({E5, F5, G5}) → J5
  42. SD({E6, F6, G6}) → J6
  43. SD({E7, F7, G7}) → J7
  44. SD({E8, F8, G8}) → J8
  45. SD({E9, F9, G9}) → J9
  46. SD({E10, F10, G10}) → J10
  47. SD({E11, F11, G11}) → J11
  48. Segment(A2, B2) → H2
  49. Segment(A3, B3) → H3
  50. Segment(A4, B4) → H4
  51. Segment(A5, B5) → H5
  52. Segment(A6, B6) → H6
  53. Segment(A7, B7) → H7
  54. Segment(A8, B8) → H8
  55. Segment(A9, B9) → H9
  56. Segment(A10, B10) → H10
  57. Segment(A11, B11) → H11
  58. Angle(D2) → α, β, γ
  59. Angle(D2) → K2, L2, M2
  60. Angle(D3) → K3, L3, M3
  61. Angle(D4) → K4, L4, M4
  62. Angle(D5) → K5, L5, M5
  63. Angle(D6) → K6, L6, M6
  64. Angle(D7) → K7, L7, M7
  65. Angle(D8) → K8, L8, M8
  66. Angle(D9) → K9, L9, M9
  67. Angle(D10) → K10, L10, M10
  68. Angle(D11) → K11, L11, M11
  69. SD({K2, L2, M2}) → I2
  70. SD({K3, L3, M3}) → I3
  71. SD({K4, L4, M4}) → I4
  72. SD({K5, L5, M5}) → I5
  73. SD({K6, L6, M6}) → I6
  74. SD({K7, L7, M7}) → I7
  75. SD({K8, L8, M8}) → I8
  76. SD({K9, L9, M9}) → I9
  77. SD({K10, L10, M10}) → I10
  78. SD({K11, L11, M11}) → I11
  79. TableText({{F1, G1, H1, I1}, {F2, G2, H2, I2}, {F3, G3, H3, I3}, {F4, G4, H4, I4}, {F5, G5, H5, I5}, {F6, G6, H6, I6}, {F7, G7, H7, I7}, {F8, G8, H8, I8}, {F9, G9, H9, I9}, {F10, G10, H10, I10}, {F11, G11, H11, I11}}, "|_") → text1
  80. SD({K2, L2, M2}) → N2
  81. SD({K3, L3, M3}) → N3
  82. SD({K4, L4, M4}) → N4
  83. SD({K5, L5, M5}) → N5
  84. SD({K6, L6, M6}) → N6
  85. SD({K7, L7, M7}) → N7
  86. SD({K8, L8, M8}) → N8
  87. SD({K9, L9, M9}) → N9
  88. SD({K10, L10, M10}) → N10
  89. SD({K11, L11, M11}) → N11
  90. TableText({{K1, L1, M1, N1}, {K2, L2, M2, N2}, {K3, L3, M3, N3}, {K4, L4, M4, N4}, {K5, L5, M5, N5}, {K6, L6, M6, N6}, {K7, L7, M7, N7}, {K8, L8, M8, N8}, {K9, L9, M9, N9}, {K10, L10, M10, N10}, {K11, L11, M11, N11}}, "|_") → text2