三角形全等的典型教材应用：对称与镜像构造

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Angle(C, B, A) → α
3. Polygon(A_1, B_1, C_1) → t1_1, c_1, a_1, b_1
4. Angle(C_1, B_1, A_1) → α_1
5. Polygon(D, E, F) → t2, f, d, e
6. Angle(D, F, E) → γ
7. Polygon(D_1, E_1, F_1) → t2_1, f_1, d_1, e_1
8. Angle(D_1, F_1, E_1) → γ_1
9. Polygon(G, H, I) → t3, i, g, h
10. Angle(G, I, H) → β
11. Polygon(G_1, H_1, I_1) → t3_1, i_1, g_1, h_1
12. Angle(G_1, I_1, H_1) → β_1
13. Polygon(J, K, L) → t4, l, j, k
14. Angle(L, K, J) → δ
15. Polygon(J_1, K_1, L_1) → t4_1, l_1, j_1, k_1
16. Angle(L_1, K_1, J_1) → δ_1
17. Polygon(M, N, O) → t5, o, m, n
18. Polygon(M_1, N_2, O_1) → t5_1, o_1, m_1, n_1
19. Mirror(M_1, n_1) → P
20. Mirror(N_2, n_1) → N_1
21. Mirror(O_1, n_1) → R
22. Polygon(P, N_1, R) → t6, r, p, q
23. Polygon(Q, S, T) → t7, t, q_1, s
24. Angle(Q, T, S) → ε
25. Angle(S, Q, T) → ζ
26. Angle(T, S, Q) → η
27. Polygon(Q_1, S_1, T_1) → t7_1, t_1, q_2, s_1
28. Angle(Q_1, T_1, S_1) → ε_1
29. Angle(S_1, Q_1, T_1) → ζ_1
30. Angle(T_1, S_1, Q_1) → η_1
31. Segment(U, U_1) → p_1
32. Midpoint(p_1) → W
33. Polygon(U, Z, W) → t8, w, u, z_1
34. Mirror(U, W) → U'
35. Mirror(Z, W) → Z_1
36. Mirror(W, W) → W'
37. Polygon(U', Z_1, W') → t8', w', u', z'
38. Angle(W, Z, U) → θ
39. Angle(W, Z_1, U_1) → ι
40. Polygon(V, P_1, R_1) → t9, r_1, v, f_2
41. Mirror(P_1, f_2) → V_1
42. Polygon(V, V_1, R_1) → t10, g_2, v_1, h_2
43. Segment(W_1, A_2) → i_2
44. Point(i_2) → B_2
45. Segment(B_2, C_2) → j_2
46. Polygon(C_2, B_2, W_1) → t11, w_1, c_2, b_2
47. Polygon(C_2, A_2, B_2) → t12, k_2, l_2, a_2
48. Angle(C_2, B_2, A_2) → λ
49. Angle(W_1, B_2, C_2) → κ
50. Polygon(D_2, E_2, F_2) → t13, m_2, d_2, e_2
51. Polygon(E_2, F_2, G_2) → t14, n_2, p_2, r_2
52. Angle(F_2, E_2, G_2) → μ
53. Angle(D_2, F_2, E_2) → ν
54. Angle(E_2, D_2, F_2) → ξ
55. Angle(E_2, G_2, F_2) → ο