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P6 Symmetry Ex5 (Two Slant Symmetrical Axes)

P6 Symmetry Ex5 (Two Slant Symmetrical Axes)
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2020-05-29 12:02
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the symmetry of geometric figures with two slant symmetrical axes. The core math concepts involved include symmetry, geometric transformations, and coordinate geometry. The construction utilizes GeoGebra commands like IndexOf, If, Segment, Mirror, Sequence, along with objects such as 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. It is suitable for high school students studying geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  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