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Rolling Triangles: Geometric Construction and Trigonometry

Rolling Triangles: Geometric Construction and Trigonometry
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2018-10-02 06:26
TriangleTrigonometryGeometric Construction
This example demonstrates the construction of multiple triangles through rotation and reflection. Key mathematical concepts include trigonometry, geometric transformations, and triangle properties. Construction involves GeoGebra commands such as Rotate, Polygon, Mirror, and Intersect, along with OrthogonalLine to determine perpendicular lines. Suitable for middle or high school mathematics education to understand geometric transformations and basic trigonometric principles.

GeoGebra Commands & Parameters

  1. Rotate((1, 0), n) → A
  2. Rotate(A, (2 * π / 3)) → A'
  3. Polygon(A, A', 3) → poly1, f, g, h, B
  4. OrthogonalLine(A', yAxis) → i
  5. OrthogonalLine(A, yAxis) → j
  6. OrthogonalLine(B, yAxis) → k
  7. Mirror(poly1, i) → poly1'
  8. OrthogonalLine(A, xAxis) → l
  9. OrthogonalLine(A', xAxis) → m
  10. Mirror(poly1, j) → poly1'_4
  11. Mirror(poly1, k) → poly1'_1
  12. Mirror(poly1, i) → poly1'_2
  13. Mirror(poly1, k) → poly1'_3
  14. Mirror(poly1, i) → poly1'_5
  15. Mirror(poly1, j) → poly1'_6
  16. Mirror(poly1, k) → poly1'_7
  17. Mirror(poly1, l) → poly1'_8
  18. OrthogonalLine(B, xAxis) → p
  19. Mirror(poly1, p) → poly1'_9
  20. Mirror(poly1, m) → poly1'_{10}
  21. Mirror(poly1, l) → poly1'_{11}
  22. Mirror(poly1, m) → poly1'_{12}
  23. Mirror(poly1, l) → poly1'_{13}
  24. Mirror(poly1, p) → poly1'_{14}
  25. Intersect(i, l) → C
  26. Intersect(j, m) → D
  27. Intersect(k, m) → E
  28. Intersect(k, l) → F
  29. Intersect(i, p) → G
  30. Intersect(j, p) → H
  31. Mirror(poly1, F) → poly1'_{15}
  32. Mirror(poly1, C) → poly1'_{16}
  33. Mirror(poly1, E) → poly1'_{17}
  34. Mirror(poly1, A') → poly1'_{18}
  35. Mirror(poly1, A) → poly1'_{19}
  36. Mirror(poly1, H) → poly1'_{20}
  37. Mirror(poly1, B) → poly1'_{21}
  38. Mirror(poly1, E) → poly1'_{22}
  39. Mirror(poly1, A') → poly1'_{23}
  40. Mirror(poly1, C) → poly1'_{24}
  41. Mirror(poly1, D) → poly1'_{25}
  42. Mirror(poly1, A) → poly1'_{26}
  43. Mirror(poly1, F) → poly1'_{27}
  44. Mirror(poly1, B) → poly1'_{28}
  45. Mirror(poly1, G) → poly1'_{29}
  46. Mirror(poly1, A') → poly1'_{30}
  47. Mirror(poly1, C) → poly1'_{31}
  48. Mirror(poly1, A) → poly1'_{32}
  49. Mirror(poly1, H) → poly1'_{33}
  50. Mirror(poly1, B) → poly1'_{34}
  51. Mirror(poly1, B) → poly1'_{35}
  52. Mirror(poly1, G) → poly1'_{36}
  53. Mirror(poly1, A') → poly1'_{37}
  54. Mirror(poly1, D) → poly1'_{38}
  55. Mirror(poly1, A) → poly1'_{39}
  56. Mirror(poly1, F) → poly1'_{40}
  57. Mirror(poly1'_{18}, l) → t1
  58. Mirror(poly1'_{25}, l) → t2
  59. Mirror(poly1'_{25}, p) → t3
  60. Mirror(poly1'_{26}, p) → t4
  61. Mirror(poly1'_{27}, p) → t5
  62. Mirror(poly1'_{27}, m) → t6
  63. Mirror(poly1'_{28}, m) → t7
  64. Mirror(poly1'_{29}, m) → t8
  65. Mirror(poly1'_{29}, l) → t9
  66. Mirror(t1, i) → t1'
  67. Mirror(t1', k) → t1''
  68. Mirror(t3, j) → t3'
  69. Mirror(t3', k) → t3''
  70. Mirror(t3, j) → t3'_1
  71. Mirror(t3'_1, i) → t10
  72. Mirror(t4, j) → t4'
  73. Mirror(t4', i) → t4''
  74. Mirror(t6, k) → t6'
  75. Mirror(t6', i) → t6''
  76. Mirror(t6, k) → t6'_1
  77. Mirror(t6'_1, j) → t11
  78. Mirror(t7, k) → t7'
  79. Mirror(t7', j) → t7''
  80. Mirror(t9, i) → t9'
  81. Mirror(t9', j) → t9''
  82. Mirror(t9, i) → t9'_1
  83. Mirror(t9'_1, k) → t12