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Symmetry Demonstration

Symmetry Demonstration
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2017-04-25 17:03
PolygonTransformationGeometric Construction
This example demonstrates the symmetry of polygons and their mirror transformations. It involves core mathematical concepts like symmetry, polygon construction, and mirror transformations. The construction uses GeoGebra commands such as Segment, Point, Polygon, Mirror, and Intersect to create polygons and perform mirror transformations. It is suitable for high school mathematics teaching to understand geometric transformations and symmetry principles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(a) → C
  3. Point(a) → J
  4. Polygon(C, D, E, F, G, H, I, J) → poly1, c, d, e, f, g, h, i, j
  5. Mirror(C, a) → C'
  6. Mirror(D, a) → D'
  7. Segment(C', D') → c'
  8. Mirror(D, a) → D'_1
  9. Mirror(E, a) → E'
  10. Segment(D'_1, E') → d'
  11. Mirror(E, a) → E'_1
  12. Mirror(F, a) → F'
  13. Segment(E'_1, F') → e'
  14. Mirror(F, a) → F'_1
  15. Mirror(G, a) → G'
  16. Segment(F'_1, G') → f'
  17. Mirror(G, a) → G'_1
  18. Mirror(H, a) → H'
  19. Segment(G'_1, H') → g'
  20. Mirror(H, a) → H'_1
  21. Mirror(I, a) → I'
  22. Segment(H'_1, I') → h'
  23. Mirror(I, a) → I'_1
  24. Mirror(J, a) → J'
  25. Segment(I'_1, J') → i'
  26. Segment(K, L) → n
  27. Point(n) → O
  28. Point(n) → V
  29. Polygon(O, P, Q, R, S, T, U, V) → poly2, o_1, p, q, r, s, t, u, v
  30. Mirror(O, n) → O'
  31. Mirror(P, n) → P'
  32. Mirror(Q, n) → Q'
  33. Mirror(R, n) → R'
  34. Mirror(S, n) → S'
  35. Mirror(T, n) → T'
  36. Mirror(U, n) → U'
  37. Mirror(V, n) → V'
  38. Polygon(O', P', Q', R', S', T', U', V') → poly2', o', p', q', r', s', t', u', v'
  39. Segment(W, Z) → c_1
  40. Point(c_1) → C_1
  41. Polygon(C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1) → poly3, c_2, d_2, e_1, f_1, g_1, h_1, i_1, j_1
  42. Mirror(C_1, c_1) → K_1
  43. Mirror(D_1, c_1) → L_1
  44. Mirror(E_1, c_1) → M_1
  45. Mirror(F_1, c_1) → N_1
  46. Mirror(G_1, c_1) → O_1
  47. Mirror(H_1, c_1) → P_1
  48. Mirror(I_1, c_1) → S_1
  49. Mirror(J_1, c_1) → T_1
  50. Polygon(K_1, L_1, M_1, N_1, O_1, P_1, S_1, T_1) → poly3', k_1, l_1, m_1, n_1, o_2, p_1, s_1, t_1
  51. Segment(U_1, V_1) → a_2
  52. Segment(W_1, Z_1) → b_2
  53. Point(b_2) → A_2
  54. Point(a_2) → G_2
  55. Intersect(a_2, b_2) → H_2
  56. Polygon(A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2) → poly4, a_3, b_3, c_3, d_3, e_2, f_2, g_2, h_2
  57. Mirror(A_2, a_2) → I_2
  58. Mirror(B_2, a_2) → J_2
  59. Mirror(C_2, a_2) → K_2
  60. Mirror(D_2, a_2) → L_2
  61. Mirror(E_2, a_2) → M_2
  62. Mirror(F_2, a_2) → N_2
  63. Mirror(G_2, a_2) → O_2
  64. Mirror(H_2, a_2) → P_2
  65. Polygon(I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2) → poly4', i_2, j_2, k_2, l_2, m_2, n_2, o_3, p_2
  66. Mirror(I_2, b_2) → Q_2
  67. Mirror(J_2, b_2) → R_2
  68. Mirror(K_2, b_2) → S_2
  69. Mirror(L_2, b_2) → T_2
  70. Mirror(M_2, b_2) → U_2
  71. Mirror(N_2, b_2) → V_2
  72. Mirror(O_2, b_2) → W_2
  73. Mirror(P_2, b_2) → Z_2
  74. Polygon(Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2) → poly4'', q_2, r_2, s_2, t_2, u_2, v_2, w_2, z_2
  75. Mirror(A_2, b_2) → A_3
  76. Mirror(B_2, b_2) → B_3
  77. Mirror(C_2, b_2) → C_3
  78. Mirror(D_2, b_2) → D_3
  79. Mirror(E_2, b_2) → E_3
  80. Mirror(F_2, b_2) → F_3
  81. Mirror(G_2, b_2) → G_3
  82. Mirror(H_2, b_2) → H_3
  83. Polygon(A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3) → poly4'_1, a_4, b_4, c_4, d_4, e_3, f_3, g_3, h_3
  84. Point(Circle[Q_3, 6]) → R_3
  85. Mirror(C, a) → C'_1
  86. Mirror(D, a) → D'_2
  87. Mirror(E, a) → E'_2
  88. Mirror(F, a) → F'_2
  89. Mirror(G, a) → G'_2
  90. Mirror(H, a) → H'_2
  91. Mirror(I, a) → I'_2
  92. Mirror(J, a) → J'_1
  93. Polygon(C'_1, D'_2, E'_2, F'_2, G'_2, H'_2, I'_2, J'_1) → poly1', c'_1, d'_2, e'_2, f'_2, g'_2, h'_2, i'_2, j'_1