多边形分类互动教学范例

多边形分类互动教学范例
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2019-07-22 15:50
该范例通过GeoGebra动态几何环境,直观展示多边形的分类及其相关术语,如边数、顶点、内角等。核心数学概念包括多边形的定义、分类(三角形、四边形、五边形等)、内角和、以及多边形与圆(半圆)的关联。作图要点:使用Polygon命令构造多个多边形(poly1、poly2),通过Segment命令绘制边,利用Intersect命令获取交点,并借助Semicircle命令构造半圆辅助观察;对象包括A、B、C、D、E、F等顶点及G、H、I、J、K等辅助点。适合初中或高中几何课堂,用于教师引导讨论、快速检测学生对多边形基础知识的掌握情况,也可作为学生自主探索多边形性质的互动工具。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  2. Polygon(G, H, I, J, K) → poly2, g, h, i, j, k
  3. Segment(M, N) → l
  4. Segment(N, L) → m
  5. Segment(L, M) → n
  6. Segment(O, P) → p
  7. Segment(P, Q) → q
  8. Segment(Q, O) → r
  9. Intersect(r, l) → R
  10. Intersect(n, r) → S
  11. Intersect(n, p) → T
  12. Intersect(p, m) → U
  13. Intersect(m, q) → V
  14. Intersect(l, q) → W
  15. Polygon(W, Q, R) → t1, r_1, w, q_1
  16. Polygon(W, N, V) → t2, v, w_1, n_1
  17. Polygon(V, P, U) → t3, u, v_1, p_1
  18. Polygon(U, L, T) → t4, t, u_1, l_1
  19. Polygon(T, O, S) → t5, s, t_1, o
  20. Polygon(S, M, R) → t6, r_2, s_1, m_1
  21. Polygon(S, T, U, V, W, R) → poly3, s_2, t_2, u_2, v_2, w_2, r_3
  22. Polygon(Z, A_1, B_1, C_1) → q1, z_1, a_1, b_1, c_1
  23. Polygon(D_1, E_1, F_1) → t7, f_1, d_1, e_1
  24. Segment(G_1, M_1) → g_1
  25. Segment(M_1, L_1) → h_1
  26. Segment(L_1, K_1) → i_1
  27. Segment(K_1, G_1) → j_1
  28. Segment(J_1, I_1) → k_1
  29. Segment(I_1, H_1) → f_2
  30. Segment(H_1, J_1) → g_2
  31. Intersect(g_2, h_1) → N_1
  32. Intersect(h_1, f_2) → O_1
  33. Intersect(i_1, f_2) → P_1
  34. Intersect(k_1, i_1) → Q_1
  35. Intersect(k_1, g_1) → R_1
  36. Intersect(g_2, g_1) → S_1
  37. Polygon(S_1, M_1, N_1) → t8, h_2, i_2, j_2
  38. Polygon(N_1, H_1, O_1) → t9, o_1, k_2, l_2
  39. Polygon(O_1, L_1, P_1) → t10, m_2, n_2, p_2
  40. Polygon(P_1, I_1, Q_1) → t11, q_2, a_2, b_2
  41. Polygon(Q_1, K_1, G_1, R_1) → q2, c_2, d_2, e_2, f_3
  42. Polygon(R_1, S_1, J_1) → t12, g_3, h_3, i_3
  43. Polygon(Q_1, P_1, O_1, N_1, S_1, R_1) → poly4, j_3, k_3, l_3, m_3, n_3, p_3
  44. Segment(T_1, U_1) → q_3
  45. Segment(U_1, V_1) → s_3
  46. Segment(V_1, W_1) → t_3
  47. Semicircle(T_1, W_1) → c_3
  48. Segment(Z_1, A_2) → a_3
  49. Segment(B_2, Z_1) → b_3
  50. Segment(B_2, C_2) → d_3
  51. Segment(D_2, C_2) → e_3
  52. Polygon(E_2, F_2, 8) → poly5, f_4, H_2, I_2, J_2, K_2, L_2, g_4, h_4, i_4, j_4, k_4, l_4, m_4, G_2
  53. Polygon(M_2, N_2, 4) → poly6, n_4, p_4, q_4, r_4, O_2, P_2