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寻找正方形与其他矩形

寻找正方形与其他矩形
几何画板及绘图内容加载中，请稍等……
2016-09-22 16:17
多边形解析几何几何作图
所属专题 dps_bhavna Sorting Geometric Figures
①本范例演示如何识别并分类正方形和矩形，并将它们拖拽到对应的灰色框中；②涉及的核心数学概念包括多边形属性、几何变换、解析几何；③作图要点——使用了Polygon（多边形）、Point（点）、Rotate（旋转）、Centroid（质心）、Ray（射线）、PointIn（点在对象内）、Segment（线段）、Mirror（镜像）、Line（直线）、Intersect（交点）、OrthogonalLine（垂线）、Circle（圆）等GeoGebra命令/对象；④适合初中及以上学生，用于几何图形识别与分类练习。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  3. Polygon(I, J, 4) → poly3, n, p, q, r, K, L
  4. Polygon(M, N, 4) → poly4, s, t, c, d, O, P
  5. Point(xAxis) → Q
  6. Point(Circle[M_1, Segment[A_1, B_1]]) → N_1
  7. Rotate(N_1 + (Segment[B_1, C_1], 0), Angle[C_1 - B_1] + Angle[N_1 - M_1] - Angle[B_1 - A_1], N_1) → O_1
  8. Rotate(O_1 + (Segment[C_1, D_1], 0), Angle[D_1 - C_1] + Angle[O_1 - N_1] - Angle[C_1 - B_1], O_1) → P_1
  9. Polygon(M_1, N_1, O_1, P_1) → poly10, m_1, n_1, o_1, p_1
  10. Point(Circle[Q_1, Segment[U, V]]) → R_1
  11. Rotate(R_1 + (Segment[V, W], 0), Angle[W - V] + Angle[R_1 - Q_1] - Angle[V - U], R_1) → S_1
  12. Rotate(S_1 + (Segment[W, Z], 0), Angle[Z - W] + Angle[S_1 - R_1] - Angle[W - V], S_1) → T_1
  13. Polygon(Q_1, R_1, S_1, T_1) → poly11, q_2, r_2, s_2, t_2
  14. Point(Circle[U_1, Segment[Q, R]]) → V_1
  15. Rotate(V_1 + (Segment[R, S], 0), Angle[S - R] + Angle[V_1 - U_1] - Angle[R - Q], V_1) → W_1
  16. Rotate(W_1 + (Segment[S, T], 0), Angle[T - S] + Angle[W_1 - V_1] - Angle[S - R], W_1) → Z_1
  17. Polygon(U_1, V_1, W_1, Z_1) → poly12, u_1, v_1, w_1, z_2
  18. Point(Circle[E_1, 1]) → F_1
  19. Polygon(E_1, F_1, G_1, H_1) → poly5, e_1, f_1, g_1, h_1
  20. Centroid(poly1) → I_1
  21. Centroid(poly2) → J_1
  22. Centroid(poly3) → K_1
  23. Centroid(poly10) → L_1
  24. Centroid(poly11) → A_2
  25. Centroid(poly12) → B_2
  26. Point(Circle[Q_2, 1.4821605850919128]) → R_2
  27. Point(Circle[U_2, 1.4598630072715726]) → V_2
  28. Point(Circle[A_3, 1.1415778554264275]) → B_3
  29. Point(Circle[E_3, 0.6596969000988258]) → F_3
  30. Point(Circle[I_3, 1]) → J_3
  31. Ray((0, 0), (1, 0)) → i_1
  32. Point(e) → M_3
  33. Point(e) → N_3
  34. Polygon(M_3, N_3, O_3, P_3) → poly14, m_3, n_3, o_3, p_3
  35. PointIn(poly14) → Q_3
  36. Point(Circle[Q_3, 1]) → R_3
  37. Segment(Q_3, R_3) → j_1
  38. Mirror(R_3, Q_3) → S_3
  39. Point(Circle[R_3, 2]) → T_3
  40. Segment(R_3, T_3) → k_1
  41. Line(T_3, S_3) → l_1
  42. Line(R_3, l_1) → a_1
  43. Line(S_3, k_1) → b_1
  44. Intersect(a_1, b_1) → U_3
  45. Polygon(T_3, R_3, U_3, S_3) → poly15, t_3, r_3, u_3, s_3
  46. PointIn(poly14) → V_3
  47. Point(Circle[V_3, 2]) → W_3
  48. Segment(V_3, W_3) → q_1
  49. Line(W_3, V_3) → r_1
  50. Point(r_1) → Z_3
  51. OrthogonalLine(V_3, q_1) → s_1
  52. Circle(V_3, Z_3) → c_1
  53. Intersect(c_1, s_1) → A_4, B_4
  54. Polygon(W_3, B_4, Z_3, A_4) → poly6, w_3, b_4, z_3, a_4
  55. PointIn(poly14) → C_4
  56. Point(Circle[C_4, 0.6]) → D_4
  57. Segment(C_4, D_4) → t_1
  58. OrthogonalLine(D_4, t_1) → d_1
  59. Mirror(D_4, C_4) → E_4
  60. Line(E_4, d_1) → f_2
  61. Circle(D_4, E_4) → c_2
  62. Intersect(c_2, d_1) → F_4, G_4
  63. Circle(E_4, C_4) → d_2
  64. Intersect(d_2, f_2) → H_4, I_4
  65. Polygon(F_4, G_4, I_4, H_4) → poly9, f_4, g_4, i_4, h_4
  66. PointIn(poly14) → J_4
  67. Point(Circle[J_4, 2]) → K_4
  68. Segment(J_4, K_4) → g_2
  69. Point(Circle[J_4, 1]) → L_4
  70. Segment(J_4, L_4) → h_2
  71. Point(Circle[J_4, 1.5]) → M_4
  72. Segment(J_4, M_4) → i_2
  73. Point(Circle[J_4, 0.9]) → N_4
  74. Segment(J_4, N_4) → j_2
  75. Polygon(M_4, K_4, L_4, N_4) → poly8, m_4, k_4, l_4, n_4
  76. PointIn(poly14) → O_4
  77. Point(Circle[O_4, 2]) → P_4
  78. Segment(O_4, P_4) → k_2
  79. Point(Circle[O_4, 1.5]) → Q_4
  80. Segment(O_4, Q_4) → l_2
  81. Point(Circle[O_4, 1]) → R_4
  82. Segment(O_4, R_4) → m_2
  83. Point(Circle[O_4, 0.7]) → S_4
  84. Segment(O_4, S_4) → n_2
  85. Polygon(P_4, R_4, Q_4, S_4) → poly13, p_4, r_4, q_4, s_4

AI 绘图提示语参考

绘制一个包含多个正方形和矩形的几何练习图。先画出四个大小不同的正方形，分别放置在画布不同位置。再构造三个由旋转生成的平行四边形，每个由一条边和旋转角度确定。接着画一个由中心点和半径确定的圆，并在圆上取点构造一个正方形。为每个多边形添加中心点标记。最后，在其中一个正方形内部随机取点，以该点为圆心画圆，通过镜像和旋转构造一个菱形，并在另一个正方形内取点画圆。整体布局用于分类识别正方形和矩形。
以上提示语为根据原始绘图命令整理而来，仅供参考。