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Rotational and Line Symmetry

Rotational and Line Symmetry
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2019-02-26 02:25
This example demonstrates rotational and line symmetry in geometric figures. It involves core math concepts like symmetry, congruence, and transformations. Key GeoGebra commands/objects used include Intersect, Point, Vector, Polygon, Segment, Circle, Line, CircleSector, Mirror, Translate, Rotate, and Angle. Suitable for high school students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Vector(A, B) → u
  4. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  5. Segment(D, B) → e
  6. Segment(A, C) → f
  7. Intersect(e, f) → O
  8. Circle(O, B) → g
  9. Point(g) → E
  10. Line(E, O) → h
  11. Intersect(g, h, 2) → F
  12. CircleSector(O, F, E) → OpaqueSemiC
  13. Mirror(list0, h) → list0'
  14. Translate(plaid, v) → plaid'
  15. Translate(O, v) → O'
  16. Translate(g, v) → g'
  17. Translate(A, v) → A'
  18. Rotate(A', (-α), O') → A''
  19. Angle(A'', O', A') → β
  20. Segment(A', O') → i
  21. Segment(A'', O') → j
  22. Rotate(plaid', (-α), O') → plaid''
  23. Translate(pic1, v) → pic1'
  24. Rotate(pic1', (-α), O') → pic1''
  25. Mirror(list1, h) → list1'
  26. Translate(h, v) → h'
  27. Point(h') → H
  28. Point(h') → I
  29. Translate(I, v) → I'
  30. Point(h) → J
  31. Point(h) → K
  32. Segment(J, K) → l
  33. Translate(J, v) → J'
  34. Translate(K, v) → K'
  35. Segment(J', K') → l'
  36. Translate(pic2, v) → pic2'
  37. Rotate(pic2', (-α), O') → pic2''
  38. Mirror(list2, h) → list2'
  39. Translate(pic3, v) → pic3'
  40. Rotate(pic3', (-α), O') → pic3''
  41. Mirror(list3, h) → list3'
  42. Translate(pic4, v) → pic4'
  43. Rotate(pic4', (-α), O') → pic4''
  44. Mirror(list4, h) → list4'
  45. Translate(pic5, v) → pic5'
  46. Rotate(pic5', (-α), O') → pic5''
  47. Mirror(list5, h) → list5'
  48. Translate(pic6, v) → pic6'
  49. Rotate(pic6', (-α), O') → pic6''
  50. Mirror(list6, h) → list6'
  51. Translate(pic7, v) → pic7'
  52. Rotate(pic7', (-α), O') → pic7''
  53. Mirror(list7, h) → list7'
  54. Translate(pic8, v) → pic8'
  55. Rotate(pic8', (-α), O') → pic8''
  56. Mirror(list8, h) → list8'
  57. Translate(pic9, v) → pic9'
  58. Rotate(pic9', (-α), O') → pic9''
  59. Mirror(list9, h) → list9'
  60. Translate(pic10, v) → pic10'
  61. Rotate(pic10', (-α), O') → pic10''
  62. Mirror(list10, h) → list10'
  63. Translate(pic11, v) → pic11'
  64. Rotate(pic11', (-α), O') → pic11''
  65. Mirror(list11, h) → list11'
  66. Translate(pic12, v) → pic12'
  67. Rotate(pic12', (-α), O') → pic12''
  68. Mirror(list12, h) → list12'
  69. Translate(pic13, v) → pic13'
  70. Rotate(pic13', (-α), O') → pic13''
  71. Mirror(list13, h) → list13'
  72. Translate(pic14, v) → pic14'
  73. Rotate(pic14', (-α), O') → pic14''
  74. Mirror(list14, h) → list14'
  75. Translate(pic15, v) → pic15'
  76. Rotate(pic15', (-α), O') → pic15''
  77. Mirror(list15, h) → list15'
  78. Translate(pic16, v) → pic16'
  79. Rotate(pic16', (-α), O') → pic16''
  80. Mirror(list16, h) → list16'