使用变换几何证明 ASA 三角形全等定理

GeoGebra 命令及参数

1. Point(Circle[A, c]) → B
2. Segment(A, B) → f
3. Rotate(B, (a * π / 180), A) → B'
4. Angle(B, A, B') → α
5. Rotate(A, (-((b * π / 180))), B) → A'
6. Angle(A', B, A) → β
7. Ray(B, B') → g
8. Ray(A, A') → h
9. Ray(A, B') → i
10. Ray(B, A') → j
11. Intersect(i, j) → C
12. Polygon(A, B, C) → t1, c_1, a_1, b_1
13. Segment(A, C) → k
14. Segment(C, B) → l
15. Min({k, l, f}) → d
16. Circle(A, (0.3 * d)) → e
17. Circle(B, (0.3 * d)) → p
18. Intersect(e, f) → D_1,
19. Intersect(e, k) → E_1,
20. Intersect(p, f) → F_1,
21. Intersect(p, l) → G,
22. CircleSector(A, D_1, E_1) → q
23. CircleSector(B, G, F_1) → r
24. Circle(D, c) → s
25. Point(s) → E
26. Segment(D, E) → m
27. Rotate(E, (a * π / 180), D) → I'
28. Angle(E, D, I') → γ
29. Rotate(D, (-((b * π / 180))), E) → H'
30. Angle(H', E, D) → δ
31. Ray(E, H') → n
32. Ray(D, I') → t
33. Intersect(n, t) → F
34. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'_1
35. Vector(A, A'_1) → u
36. Translate(q, u) → q'
37. Line(D, k) → f_1
38. Point(f_1) → K
39. Angle(F, D, K) → ε
40. Rotate(q', If[1 < o ≤ 2, ((-(o - 1)) * ε), (-ε)], D) → q''
41. Translate(A, u) → A'_2
42. Translate(B, u) → B'_1
43. Segment(A'_2, B'_1) → f'
44. Translate(r, u) → r'
45. Rotate(A'_2, If[1 < o ≤ 2, ((-(o - 1)) * ε), (-ε)], D) → L
46. Rotate(B'_1, If[1 < o ≤ 2, ((-(o - 1)) * ε), (-ε)], D) → M
47. Segment(L, M) → f''
48. Rotate(r', If[1 < o ≤ 2, ((-(o - 1)) * ε), (-ε)], D) → r''
49. Ray(A, C) → g_1
50. Ray(B, C) → h_1
51. Translate(A, u) → A'_3
52. Translate(C, u) → C'
53. Translate(B, u) → B'_2
54. Translate(C, u) → C'_1
55. Angle(H, I, J) → ζ