莫利三角形定理的动态演示与证明

GeoGebra 命令及参数

1. Polygon(A, B, C) → polígono1, c, a, b
2. Angle(polígono1) → α_3, β_3, γ_3
3. Rotate(B, α_3 / 3, A) → B'
4. Rotate(B, (2 * α_3 / 3), A) → B'_1
5. Rotate(C, β_3 / 3, B) → C'
6. Rotate(C, (2 * β_3 / 3), B) → C'_1
7. Rotate(A, γ_3 / 3, C) → A'
8. Rotate(A, (2 * γ_3 / 3), C) → A'_1
9. Ray(A, B') → f
10. Ray(A, B'_1) → g
11. Ray(B, C') → h
12. Ray(B, C'_1) → i
13. Ray(C, A') → j
14. Ray(C, A'_1) → k
15. Intersect(f, i) → Z
16. Intersect(h, k) → X
17. Intersect(g, j) → Y
18. Polygon(Y, Z, X) → polígono2, e, f_1, d
19. Angle(B, A, Z) → α
20. Angle(Z, A, Y) → α_1
21. Angle(Y, A, C) → α_2
22. Angle(C, B, C') → β
23. Angle(C', B, C'_1) → β_1
24. Angle(C'_1, B, A) → β_2
25. Angle(A, C, A') → γ
26. Angle(A', C, A'_1) → γ_1
27. Angle(A'_1, C, B) → γ_2
28. Intersect(g, h) → U
29. Circle(Y, X, C) → w
30. Intersect(w, b, 2) → X'
31. Intersect(w, a, 2) → Y'
32. Segment(U, Z) → l
33. Angle(X, Z, U) → δ
34. Angle(U, Z, Y) → ε
35. Segment(A, Z) → m
36. Segment(A, U) → n
37. Segment(B, U) → q
38. Segment(B, Z) → r
39. Segment(C, Y) → s
40. Segment(C, X) → t
41. Segment(A, Y) → g_1
42. Segment(B, X) → h_1
43. Angle(X, Z, Y) → ζ
44. Segment(Y, X') → i_1
45. Segment(X, Y') → j_1
46. Angle(Y', X, Y) → η
47. Angle(X, Y, X') → θ
48. Center(w) → O
49. Segment(X', O) → k_1
50. Segment(O, Y) → l_1
51. Segment(O, X) → m_1
52. Segment(O, Y') → n_1
53. Angle(X', O, Y) → ι
54. Angle(Y, O, X) → κ
55. Angle(X, O, Y') → λ
56. Segment(X', Y') → p