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Drawing Lines of Symmetry with Polygon Mirroring in GeoGebra

Drawing Lines of Symmetry with Polygon Mirroring in GeoGebra
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2012-08-17 15:06
PolygonTransformationGeometric Construction
In collections CBSE Class VI Maths Flip & turn
This GeoGebra example demonstrates how to construct polygons and their mirror images across a line of symmetry, offering a dynamic visualization of axial symmetry and reflection. The core mathematical concepts involved are symmetry, reflection transformation, polygons, and line segments. The construction uses the Polygon command to create polygon objects such as poly1, poly2, and poly3, the Mirror command to generate reflected figures across the symmetry axis, and the Segment command to draw the axis and related segments; points A through S and segment labels a–m, n–r are included. It is suitable for middle school and high school geometry instruction, classroom demonstrations of symmetric properties, and student-centered exploration of geometric transformations.

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