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四边形分类 by Anthony OR 柯志明

四边形分类 by Anthony OR 柯志明
几何画板及绘图内容加载中，请稍等……
2012-10-14 11:45
多边形向量几何作图
所属专题 CBSE Class VI Maths
本 GeoGebra 范例通过动态着色方式演示四边形的分类方法，帮助学生直观识别和区分不同类型的四边形，如正方形、矩形、平行四边形和梯形。涉及的核心数学概念包括四边形的几何性质、分类标准（如边平行性、角特征）以及空间推理能力。作图要点：使用了 Point 命令定义点对象（如 A'、B、C、D），Polygon 命令绘制多边形（如 polyA、poly1、poly2），以及 UnitVector 和 UnitOrthogonalVector 命令辅助方向向量构造，从而构建出完整的四边形分类模型。适合初中或高中几何课程，可用于课堂教学或学生自主学习。

GeoGebra 命令及参数

  1. Point(Circle[A', 4]) → B
  2. Polygon(A', B, C, D) → polyA, a_1, a_2, a_3, a_4
  3. Point(Circle[E, 0.3999999999999986]) → F
  4. Polygon(E, F, G, H) → poly2, e, f, g, h
  5. Point(Circle[I, 0.3000000000000007]) → J
  6. Polygon(I, J, K, L) → poly1, i, j, k, l
  7. Point(Circle[M, 0.3000000000000007]) → N
  8. Polygon(M, N, O, P) → poly4, m, n, o, p
  9. Point(Circle[Q, 0.3605551275463988]) → R
  10. Polygon(Q, R, S, T) → poly3, q, r, s, t
  11. Point(Circle[U, 0.5]) → V
  12. Polygon(U, V, W, Z) → poly5, u', v', w, z
  13. Point(Circle[A'_1, 0.3999999999999986]) → B_1
  14. Polygon(A'_1, B_1, C_1, D_1) → poly6, a_5, b_5, c_5, d_5
  15. Point(Circle[E_1, 2]) → F_1
  16. Polygon(E_1, F_1, G_1, H_1) → polyB, b_1, b_2, b_3, b_4
  17. Point(Circle[I_1, 1]) → J_1
  18. Polygon(I_1, J_1, K_1, L_1) → polyC, c_1, c_2, c_3, c_4
  19. Point(Circle[M_1, 1.9849433241279208]) → N_1
  20. Polygon(M_1, N_1, O_1, P_1) → polyD, d_1, d_2, d_3, d_4
  21. Point(Circle[Q_1, 1.5]) → R_1
  22. Polygon(Q_1, R_1, S_1, T_1) → polyE, e_1, e_2, e_3, e_4
  23. Point(Circle[U_1, 4.5]) → V_1
  24. Polygon(U_1, V_1, W_1, Z_1) → polyF, f_1, f_2, f_3, f_4
  25. Point(Circle[A'_2, 1.47648230602334]) → B_2
  26. Polygon(A'_2, B_2, C_2, D_2) → polyG, g_2, g_1, g_3, g_4
  27. Point(Circle[E_2, 3]) → F_2
  28. Polygon(E_2, F_2, G_2, H_2) → polyH, h_1, h_2, h_4, h_3
  29. Point(Circle[I_2, 3]) → J_2
  30. Polygon(I_2, J_2, K_2, L_2) → polyI, i_1, i_2, i_3, i_4
  31. Point(Circle[M_2, 3.0083217912982647]) → N_2
  32. Polygon(M_2, N_2, O_2, P_2) → polyJ, j_1, j_2, j_3, j_4
  33. Point(Circle[Q_2, 1.6]) → R_2
  34. Polygon(Q_2, R_2, S_2, T_2) → polyK, k_1, k_2, k_3, k_4
  35. Point(Circle[U_2, 1.5]) → V_2
  36. Polygon(U_2, V_2, W_2, Z_2) → polyL, l_1, l_2, l_3, l_4
  37. Point(Circle[A'_3, 1.5]) → B_3
  38. Polygon(A'_3, B_3, C_3, D_3) → polyM, m_1, m_2, m_3, m_4
  39. Point(Circle[E_3, 2.5]) → F_3
  40. Polygon(E_3, F_3, G_3, H_3) → polyN, n_1, n_2, n_3, n_4
  41. Point(Circle[I_3, 2]) → J_3
  42. Polygon(I_3, J_3, K_3, L_3) → polyO, o_1, o_2, o_3, o_4
  43. Point(Circle[M_3, 5.5]) → N_3
  44. Polygon(M_3, N_3, O_3, P_3) → polyP, p_1, p_4, p_2, p_3
  45. Point(Circle[Q_3, 2]) → R_3
  46. Polygon(Q_3, R_3, S_3, T_3) → polyQ, q_1, q_2, q_3, q_4
  47. Point(Circle[U_3, 2.5]) → V_3
  48. Polygon(U_3, V_3, W_3, Z_3) → polyR, r_1, r_2, r_3, r_4
  49. Point(Circle[A'_4, 1.2]) → B_4
  50. Polygon(A'_4, B_4, C_4, D_4) → polyS, s_1, s_2, s_3, s_4
  51. Point(Circle[E_4, 1.5]) → F_4
  52. Polygon(E_4, F_4, G_4, H_4) → polyT, t_1, t_2, t_3, t_4
  53. Polygon(I_4, J_4, K_4, L_4) → poly7, i_5, j_5, k_5, l_5
  54. Polygon(I_5, J_5, K_5, L_5) → poly7_1, i_6, j_6, k_6, l_6
  55. Polygon(I_6, J_6, K_6, L_6) → poly7_2, i_7, j_7, k_7, l_7
  56. Polygon(I_7, J_7, K_7, L_7) → poly7_3, i_8, j_8, k_8, l_8
  57. Polygon(I_8, J_8, K_8, L_8) → poly7_4, i_9, j_9, k_9, l_9
  58. Polygon(I_9, J_9, K_9, L_9) → poly7_5, i_{10}, j_{10}, k_{10}, l_{10}
  59. Point(Circle[A_1, 1]) → A_6
  60. UnitVector(Segment[A_1, A_6]) → u
  61. UnitOrthogonalVector(Segment[A_1, A_6]) → v
  62. Polygon(A_1, A_2, A_3, A_4, A_5, A_6) → poly8, a_6, a_7, a_8, a_9, a_{10}, a_{11}