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Hexagon Construction Example

Hexagon Construction Example
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2020-03-11 22:54
PolygonAngleVectorGeometric Construction
This example demonstrates the geometric construction of a hexagon and its related transformations. It involves core mathematical concepts such as polygons, angles, vectors, rotation, reflection, translation, midpoint, centroid, and line intersections. The construction utilizes GeoGebra commands like Polygon, Midpoint, Centroid, Line, Rotate, Angle, Mirror, Intersect, Vector, and Translate. It is suitable for high school mathematics education, showcasing geometric transformations and construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  2. Midpoint(D, E) → G
  3. Midpoint(E, F) → H
  4. Midpoint(F, A) → I
  5. Midpoint(A, B) → J
  6. Midpoint(B, C) → K
  7. Midpoint(C, D) → L
  8. Centroid(poly1) → M
  9. Line(D, C) → l
  10. Rotate(l, (-α), L) → l'
  11. Angle(l', l) → γ
  12. Rotate(l', 60°, M) → l''
  13. Rotate(l'', 60°, M) → l'''
  14. Rotate(l''', 60°, M) → m
  15. Rotate(m, 60°, M) → m'
  16. Rotate(m', 60°, M) → m''
  17. Mirror(l', h) → l''_1
  18. Mirror(m'', g) → m'''
  19. Mirror(m', f) → m''_1
  20. Mirror(m, k) → m'_1
  21. Mirror(l''', j) → n
  22. Mirror(l'', i) → l'''_1
  23. Intersect(l'', l''_1) → N
  24. Intersect(l'', l''_1) → O
  25. Intersect(l', m''') → P
  26. Intersect(m'', m''_1) → Q
  27. Intersect(m', m'_1) → R
  28. Intersect(m, n) → S
  29. Intersect(l''', l'''_1) → T
  30. Polygon(L, N, K, P, G, T, H, S, I, R, J, Q) → poly2, l_1, q, k_1, p, n_1, g_1, t, h_1, s, i_1, r, j_1
  31. Polygon(B, A, 6) → poly3, a, Z, b, c, d, e, f_1, U, V, W
  32. Polygon(U, A, 6) → poly4, m_1, D_1, p_1, q_1, r_1, s_1, t_1, A_1, B_1, C_1
  33. Vector(D, B) → u
  34. Translate(L, u) → L'
  35. Translate(N, u) → N'
  36. Translate(G, u) → G'
  37. Translate(T, u) → T'
  38. Translate(H, u) → H'
  39. Translate(S, u) → S'
  40. Translate(I, u) → I'
  41. Translate(R, u) → R'
  42. Translate(J, u) → J'
  43. Translate(Q, u) → Q'
  44. Translate(K, u) → K'
  45. Translate(P, u) → P'
  46. Polygon(L', N', K', P', G', T', H', S', I', R', J', Q') → poly2', l'_1, q', k', p', n', g', t', h', s', i', r', j'
  47. Translate(D, v) → D'
  48. Translate(B, v) → B'
  49. Vector(D, F) → w
  50. Translate(L, w) → L'_1
  51. Translate(N, w) → N'_1
  52. Translate(G, w) → G'_1
  53. Translate(T, w) → T'_1
  54. Translate(H, w) → H'_1
  55. Translate(S, w) → S'_1
  56. Translate(I, w) → I'_1
  57. Translate(R, w) → R'_1
  58. Translate(J, w) → J'_1
  59. Translate(Q, w) → Q'_1
  60. Translate(K, w) → K'_1
  61. Translate(P, w) → P'_1
  62. Polygon(L'_1, N'_1, K'_1, P'_1, G'_1, T'_1, H'_1, S'_1, I'_1, R'_1, J'_1, Q'_1) → poly2'', l'_2, q'_1, k'_1, p'_1, n'_1, g'_1, t'_1, h'_1, s'_1, i'_1, r'_1, j'_1
  63. Polygon(W, V, 6) → poly5, a_1, H_1, b_1, c_1, d_1, e_1, f_2, E_1, F_1, G_1
  64. Polygon(U, D_1, 6) → poly6, g_2, L_1, h_2, i_2, j_2, k_2, l_2, I_1, J_1, K_1
  65. Translate(L', u) → L''
  66. Translate(N', u) → N''
  67. Translate(G', u) → G''
  68. Translate(T', u) → T''
  69. Translate(H', u) → H''
  70. Translate(S', u) → S''
  71. Translate(I', u) → I''
  72. Translate(R', u) → R''
  73. Translate(J', u) → J''
  74. Translate(Q', u) → Q''
  75. Translate(K', u) → K''
  76. Translate(P', u) → P''
  77. Polygon(L'', N'', K'', P'', G'', T'', H'', S'', I'', R'', J'', Q'') → poly2''_1, l''_2, q'', k'', p'', n'', g'', t'', h'', s'', i'', r'', j''
  78. Vector(W, U) → u_1
  79. Translate(L'', u_1) → L'''
  80. Translate(N'', u_1) → N'''
  81. Translate(G'', u_1) → G'''
  82. Translate(T'', u_1) → T'''
  83. Translate(H'', u_1) → H'''
  84. Translate(S'', u_1) → S'''
  85. Translate(I'', u_1) → I'''
  86. Translate(R'', u_1) → R'''
  87. Translate(J'', u_1) → J'''
  88. Translate(Q'', u_1) → Q'''
  89. Translate(K'', u_1) → K'''
  90. Translate(P'', u_1) → P'''
  91. Polygon(L''', N''', K''', P''', G''', T''', H''', S''', I''', R''', J''', Q''') → poly7, l'''_2, q''', k''', p''', n''', g''', t''', h''', s''', i''', r''', j'''