对称性图形与作图方法

对称性图形与作图方法
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2020-10-20 12:01
本范例演示了对称性图形的构造与分析,涉及对称轴、三角形、圆、多边形等几何概念。作图要点包括使用GeoGebra命令如Segment、Polygon、Line、Circle等来创建对称图形。适合初中及以上数学学习者,用于理解几何对称性和图形变换。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个包含多种对称图形的几何构图。先画一个三角形,再画一个四边形,接着画一个五边形,并分别用线段连接它们的顶点。然后画一条穿过图形的对称轴直线,再画一个圆,在圆上取两点并绘制圆弧。最后画一个由线段和圆弧组成的组合图形,并添加一条辅助直线。整体展示对称轴、三角形、圆和多边形的组合关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。