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Lines of symmetry

Lines of symmetry
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2020-10-20 12:01
TriangleCirclePolygonGeometric Construction
This example demonstrates the construction and analysis of symmetry figures, involving concepts like symmetry axes, triangles, circles, and polygons. The construction uses GeoGebra commands such as Segment, Polygon, Line, Circle, etc. It is suitable for middle school and above students to understand geometric symmetry and transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, D) → b
  3. Segment(A, C) → c
  4. Segment(E, C) → d
  5. Segment(D, F) → e
  6. Segment(F, G) → f
  7. Segment(E, G) → g
  8. Segment(H, I) → h
  9. Polygon(J, K, L) → poly1, l, j, k
  10. Segment(M, N) → i
  11. Segment(O, N) → m
  12. Segment(M, O) → n
  13. Segment(P, Q) → p
  14. Segment(P, R) → q
  15. Segment(Q, S) → r
  16. Segment(R, T) → s
  17. Segment(S, U) → t
  18. Segment(T, U) → a_1
  19. Line(V, W) → b_1
  20. Segment(Z, A_1) → c_1
  21. Line(B_1, C_1) → d_1
  22. Line(D_1, E_1) → e_1
  23. Segment(F_1, G_1) → f_1
  24. Segment(H_1, I_1) → g_1
  25. Line(J_1, K_1) → h_1
  26. Segment(L_1, M_1) → i_1
  27. Segment(M_1, N_1) → j_1
  28. Segment(L_1, O_1) → k_1
  29. Segment(O_1, P_1) → l_1
  30. Segment(N_1, Q_1) → m_1
  31. Segment(P_1, R_1) → n_1
  32. Segment(Q_1, S_1) → p_1
  33. Segment(R_1, T_1) → q_1
  34. Segment(T_1, S_1) → r_1
  35. Segment(U_1, V_1) → s_1
  36. Line(W_1, Z_1) → t_1
  37. Circle(A_2, B_2) → c_2
  38. Point(c_2) → C_2
  39. Point(c_2) → E_2
  40. CircumcircleArc(C_2, D_2, E_2) → d_2
  41. CircumcircleArc(C_2, F_2, E_2) → e_2
  42. Line(G_2, H_2) → a_2
  43. Segment(I_2, J_2) → b_2
  44. CircumcircleArc(K_2, L_2, M_2) → f_2
  45. Circle(N_2, L_2) → g_2
  46. Segment(K_2, N_2) → h_2
  47. Segment(N_2, M_2) → i_2
  48. Line(O_2, P_2) → j_2
  49. Segment(Q_2, R_2) → k_2
  50. Circle(S_2, T_2) → p_2
  51. Point(p_2) → U_2
  52. Point(p_2) → W_2
  53. CircumcircleArc(T_2, W_2, U_2) → q_2
  54. Segment(V_2, T_2) → l_2
  55. Segment(V_2, U_2) → m_2
  56. Polygon(V_2, T_2, U_2) → poly2, u_2, v_2, t_2
  57. Segment(Z_2, A_3) → n_2
  58. Line(B_3, C_3) → r_2
  59. Polygon(D_3, E_3, F_3, G_3) → poly3, d_3, e_3, f_3, g_3
  60. Polygon(F_3, J_3, K_3, G_3) → poly4, f_4, j_3, k_3, g_4
  61. Polygon(F_3, I_3, H_3, E_3) → poly5, f_5, i_3, h_3, e_4
  62. Polygon(L_3, M_3, N_3, O_3) → poly6, l_3, m_3, n_3, o_3
  63. Polygon(O_3, P_3, Q_3, R_3) → poly7, o_1, p_3, q_3, r_3
  64. Polygon(Q_3, S_3, T_3, U_3) → poly8, q_4, s_3, t_3, u_3
  65. Point(m_3) → W_3
  66. Polygon(M_3, V_3, T_3, W_3) → poly9, m_4, v_3, t_4, w_3
  67. Polygon(Z_3, A_4, B_4, C_4) → poly10, z_3, a_4, b_4, c_4
  68. Point(a_4) → E_4
  69. Polygon(D_4, E_4, F_4, G_4) → poly11, d_4, e_5, f_6, g_5
  70. Polygon(H_4, I_4, J_4, K_4) → poly12, h_4, i_4, j_4, k_4
  71. Point(i_4) → L_4
  72. Polygon(L_4, M_4, N_4, O_4) → poly13, l_4, m_5, n_4, o_4
  73. Polygon(P_4, Q_4, B_5, C_5, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5) → poly14, p_4, a_5, b_5, c_5, q_5, r_4, s_4, t_5, u_4, v_4, w_4, z_4
  74. Segment(D_5, E_5) → s_2
  75. Segment(F_5, G_5) → a_3
  76. Segment(H_5, I_5) → b_3
  77. Segment(J_5, K_5) → c_3
  78. Line(L_5, M_5) → d_5
  79. Line(N_5, O_5) → h_5
  80. Line(P_5, Q_5) → i_5
  81. Line(R_5, S_5) → j_5
  82. Segment(T_5, U_5) → k_5
  83. Segment(V_5, W_5) → l_5
  84. Line(Z_5, A_6) → n_5
  85. Line(B_6, C_6) → p_5

AI Drawing Prompt Reference

Draw a geometric composition featuring multiple symmetric shapes. Start with a triangle, then a quadrilateral, followed by a pentagon, connecting their vertices with line segments. Add a symmetry axis line through the figures, then draw a circle with two points on it and create arcs. Finally, construct a combined shape using segments and arcs, and include an auxiliary line. The overall design illustrates symmetry axes, triangles, circles, and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.