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Symmetry Lines Demonstration

Symmetry Lines Demonstration
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2019-01-21 03:46
PolygonTransformationGeometric Construction
This example demonstrates how to draw symmetry lines of polygons and observe their symmetry properties. It involves core math concepts like symmetry axes, symmetry, and polygonal geometric properties. Constructed using GeoGebra commands and objects such as Polygon, Mirror, and Segment. Suitable for middle school and above students to learn and understand geometric symmetry, ideal for math teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  2. Polygon(G, H, I, J, K, L, M) → poly2, g, h, i, j, k, l, m
  3. Polygon(N, O, P, Q, R, S) → poly3, n, o, p, q, r, s
  4. Polygon(T, U, V, W, Z, A_1, B_1) → poly4, t, u, v, w, z, a_1, b_1
  5. Polygon(C_1, E_1, O_1, P_1, Q_1, R_1, F_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1) → poly5, c_1, n_1, o_1, p_1, q_1, r_1, e_1, f_1, h_1, i_1, j_1, k_1, l_1, m_1
  6. Polygon(G_1, S_1, E_2, F_2, G_2, H_2, I_2, J_2, T_1, U_1, V_1, W_1, Z_1, B_2, C_2, D_2) → poly6, g_1, d_2, e_2, f_2, g_2, h_2, i_2, j_2, s_1, t_1, u_1, v_1, w_1, z_1, b_2, c_2
  7. Mirror(A, f) → A'
  8. Mirror(B, f) → B'
  9. Mirror(C, f) → C'
  10. Mirror(D, f) → D'
  11. Mirror(E, f) → E'
  12. Mirror(F, f) → F'
  13. Polygon(A', B', C', D', E', F') → poly1', a', b', c', d', e', f'
  14. Mirror(G, k) → G'
  15. Mirror(H, k) → H'
  16. Mirror(I, k) → I'
  17. Mirror(J, k) → J'
  18. Mirror(K, k) → K'
  19. Mirror(L, k) → L'
  20. Mirror(M, k) → M'
  21. Polygon(G', H', I', J', K', L', M') → poly2', g', h', i', j', k', l', m'
  22. Mirror(N, n) → N'
  23. Mirror(O, n) → O'
  24. Mirror(P, n) → P'
  25. Mirror(Q, n) → Q'
  26. Mirror(R, n) → R'
  27. Mirror(S, n) → S'
  28. Polygon(N', O', P', Q', R', S') → poly3', n', o', p', q', r', s'
  29. Mirror(T, v) → T'
  30. Mirror(U, v) → U'
  31. Mirror(V, v) → V'
  32. Mirror(W, v) → W'
  33. Mirror(Z, v) → Z'
  34. Mirror(A_1, v) → A_2
  35. Mirror(B_1, v) → K_2
  36. Polygon(T', U', V', W', Z', A_2, K_2) → poly4', t', u', v', w', z', a_2, k_2
  37. Mirror(C_1, r_1) → L_2
  38. Mirror(E_1, r_1) → M_2
  39. Mirror(F_1, r_1) → N_2
  40. Mirror(H_1, r_1) → O_2
  41. Mirror(I_1, r_1) → P_2
  42. Mirror(J_1, r_1) → Q_2
  43. Mirror(K_1, r_1) → R_2
  44. Mirror(L_1, r_1) → S_2
  45. Mirror(M_1, r_1) → T_2
  46. Mirror(N_1, r_1) → U_2
  47. Mirror(O_1, r_1) → V_2
  48. Mirror(P_1, r_1) → W_2
  49. Mirror(Q_1, r_1) → Z_2
  50. Mirror(R_1, r_1) → A_3
  51. Polygon(L_2, M_2, V_2, W_2, Z_2, A_3, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2) → poly5', l_2, u_2, v_2, w_2, z_2, a_3, m_2, n_2, o_2, p_2, q_2, r_2, s_2, t_2
  52. Mirror(G_1, h_2) → B_3
  53. Mirror(S_1, h_2) → C_3
  54. Mirror(T_1, h_2) → D_3
  55. Mirror(U_1, h_2) → E_3
  56. Mirror(V_1, h_2) → F_3
  57. Mirror(W_1, h_2) → G_3
  58. Mirror(Z_1, h_2) → H_3
  59. Mirror(B_2, h_2) → I_3
  60. Mirror(C_2, h_2) → J_3
  61. Mirror(D_2, h_2) → K_3
  62. Mirror(E_2, h_2) → L_3
  63. Mirror(F_2, h_2) → M_3
  64. Mirror(G_2, h_2) → N_3
  65. Mirror(H_2, h_2) → O_3
  66. Mirror(I_2, h_2) → P_3
  67. Mirror(J_2, h_2) → Q_3
  68. Polygon(B_3, C_3, L_3, M_3, N_3, O_3, P_3, Q_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3) → poly6', b_3, k_3, l_3, m_3, n_3, o_3, p_3, q_3, c_3, d_3, e_3, f_3, g_3, h_3, i_3, j_3
  69. Segment(R_3, S_3) → d_1
  70. Segment(T_3, U_3) → r_3
  71. Segment(V_3, W_3) → s_3
  72. Segment(Z_3, A_4) → t_3
  73. Segment(B_4, D_1) → a_4
  74. Segment(C_4, D_4) → b_4