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P6对称题五（两个倾斜的对称轴）

P6对称题五（两个倾斜的对称轴）
几何画板及绘图内容加载中，请稍等……
2020-05-29 11:57
解析几何变换几何作图
所属专题 P6 6S1 对称 (中文版)
①本范例演示了具有两个倾斜对称轴的图形对称性；②涉及的核心数学概念包括对称性、几何变换、坐标几何；③作图要点：使用了GeoGebra命令Indexof, If, Segment, Mirror, Sequence，以及对象SymA4, SymA2, Blue10a, ListSymA, NumSymA, SymB, SymA3, SymA1, SymA, Blue10b, Blue10, Blue8a, Blue8b, Blue8, Blue6a, Blue6b, Blue6, Blue4a, Blue4b, Blue4, Blue2a, Blue2b, Blue2, Blue1b, Blue10b1, Blue10a1, Ref1Blue10, Blue8a1, Blue8b1, Ref1Blue08, Blue6a1, Blue6b1, Ref1Blue06, Blue4a1, Blue4b1, Ref1Blue04, Blue2a1, Blue2b1, Ref1Blue02, Blue1b1；④适合初中及以上学段学习几何变换与对称性，可用于教学演示和习题设计。

GeoGebra 命令及参数

  1. IndexOf(SelectedElement[ListSymA], ListSymA) → NumSymA
  2. If(NumSymA ≟ 1, SymA2, SymA4) → SymB
  3. If(NumSymA ≟ 1, SymA1, SymA3) → SymA
  4. Segment(Blue10a, Blue10b) → Blue10
  5. Segment(Blue8a, Blue8b) → Blue8
  6. Segment(Blue6a, Blue6b) → Blue6
  7. Segment(Blue4a, Blue4b) → Blue4
  8. Segment(Blue2a, Blue2b) → Blue2
  9. Mirror(Blue10b, SymA) → Blue10b1
  10. Mirror(Blue10a, SymA) → Blue10a1
  11. Segment(Blue10a1, Blue10b1) → Ref1Blue10
  12. Mirror(Blue8a, SymA) → Blue8a1
  13. Mirror(Blue8b, SymA) → Blue8b1
  14. Segment(Blue8a1, Blue8b1) → Ref1Blue08
  15. Mirror(Blue6a, SymA) → Blue6a1
  16. Mirror(Blue6b, SymA) → Blue6b1
  17. Segment(Blue6a1, Blue6b1) → Ref1Blue06
  18. Mirror(Blue4a, SymA) → Blue4a1
  19. Mirror(Blue4b, SymA) → Blue4b1
  20. Segment(Blue4a1, Blue4b1) → Ref1Blue04
  21. Mirror(Blue2a, SymA) → Blue2a1
  22. Mirror(Blue2b, SymA) → Blue2b1
  23. Segment(Blue2a1, Blue2b1) → Ref1Blue02
  24. Mirror(Blue1b, SymA) → Blue1b1
  25. Mirror(Blue10b, SymB) → Blue10b2
  26. Mirror(Blue10a, SymB) → Blue10a2
  27. Segment(Blue10a2, Blue10b2) → Ref2Blue10
  28. Mirror(Blue8a, SymB) → Blue8a2
  29. Mirror(Blue8b, SymB) → Blue8b2
  30. Segment(Blue8a2, Blue8b2) → Ref2Blue08
  31. Mirror(Blue6a, SymB) → Blue6a2
  32. Mirror(Blue6b, SymB) → Blue6b2
  33. Segment(Blue6a2, Blue6b2) → Ref2Blue06
  34. Mirror(Blue4a, SymB) → Blue4a2
  35. Mirror(Blue4b, SymB) → Blue4b2
  36. Segment(Blue4a2, Blue4b2) → Ref2Blue04
  37. Mirror(Blue2a, SymB) → Blue2a2
  38. Mirror(Blue2b, SymB) → Blue2b2
  39. Segment(Blue2a2, Blue2b2) → Ref2Blue02
  40. Mirror(Blue1b, SymB) → Blue1b2
  41. Segment(Blue1a, Blue1b) → Blue1
  42. Mirror(Blue1a, SymA) → Blue1a1
  43. Segment(Blue1a1, Blue1b1) → Ref1Blue01
  44. Mirror(Blue1a, SymB) → Blue1a2
  45. Segment(Blue1a2, Blue1b2) → Ref2Blue01
  46. Mirror(Blue3b, SymA) → Blue3b1
  47. Mirror(Blue3b, SymB) → Blue3b2
  48. Mirror(Blue3a, SymA) → Blue3a1
  49. Segment(Blue3a1, Blue3b1) → Ref1Blue03
  50. Mirror(Blue3a, SymB) → Blue3a2
  51. Segment(Blue3a2, Blue3b2) → Ref2Blue03
  52. Segment(Blue3a, Blue3b) → Blue3
  53. Mirror(Blue5b, SymA) → Blue5b1
  54. Mirror(Blue5b, SymB) → Blue5b2
  55. Mirror(Blue5a, SymA) → Blue5a1
  56. Segment(Blue5a1, Blue5b1) → Ref1Blue05
  57. Mirror(Blue5a, SymB) → Blue5a2
  58. Segment(Blue5a2, Blue5b2) → Ref2Blue05
  59. Segment(Blue5a, Blue5b) → Blue5
  60. Mirror(Blue7b, SymA) → Blue7b1
  61. Mirror(Blue7b, SymB) → Blue7b2
  62. Mirror(Blue7a, SymA) → Blue7a1
  63. Segment(Blue7a1, Blue7b1) → Ref1Blue07
  64. Mirror(Blue7a, SymB) → Blue7a2
  65. Segment(Blue7a2, Blue7b2) → Ref2Blue07
  66. Segment(Blue7a, Blue7b) → Blue7
  67. Mirror(Blue9b, SymA) → Blue9b1
  68. Mirror(Blue9b, SymB) → Blue9b2
  69. Mirror(Blue9a, SymA) → Blue9a1
  70. Segment(Blue9a1, Blue9b1) → Ref1Blue09
  71. Mirror(Blue9a, SymB) → Blue9a2
  72. Segment(Blue9a2, Blue9b2) → Ref2Blue09
  73. Segment(Blue9a, Blue9b) → Blue9
  74. IndexOf(SelectedElement[ListNumSeg], ListNumSeg) → NumSeg
  75. Sequence(Sequence[(s, t), s, -14, 12], t, -8, 8) → ListDots
  76. Segment(Blue11a, Blue11b) → Blue11
  77. Segment(Blue12a, Blue12b) → Blue12
  78. Mirror(Blue11a, SymA) → Blue11a1
  79. Mirror(Blue11b, SymA) → Blue11b1
  80. Mirror(Blue12a, SymA) → Blue12a1
  81. Mirror(Blue12b, SymA) → Blue12b1
  82. Segment(Blue11a1, Blue11b1) → Ref1Blue11
  83. Segment(Blue12a1, Blue12b1) → Ref1Blue12
  84. Mirror(Blue11a, SymB) → Blue11a2
  85. Mirror(Blue11b, SymB) → Blue11b2
  86. Mirror(Blue12a, SymB) → Blue12a2
  87. Mirror(Blue12b, SymB) → Blue12b2
  88. Segment(Blue11a2, Blue11b2) → Ref2Blue11
  89. Segment(Blue12a2, Blue12b2) → Ref2Blue12
  90. If(NumSeg ≟ 1, Match1, NumSeg ≟ 6, Match6, NumSeg ≟ 7, Match7, NumSeg ≟ 8, Match8, NumSeg ≟ 9, Match9, NumSeg ≟ 10, Match10, NumSeg ≟ 2, NumSeg ≟ 11, Match11, Match12, Match2, NumSeg ≟ 3, Match3, NumSeg ≟ 4, Match4, NumSeg ≟ 5, Match5) → Match