等角三角形必为等边三角形（逆定理II）动态演示

GeoGebra 命令及参数

1. Line(A, B) → f
2. Ray(A, B) → g
3. Point(g) → C
4. Rotate(C, π / 3, A) → C'
5. Angle(C, A, C') → α
6. Rotate(A, (-(π / 3)), C) → A'
7. Angle(A', C, A) → β
8. Circle(A, C) → c
9. Circle(C, A) → d
10. Intersect(c, d, 1) → D
11. Segment(A, D) → h
12. Segment(A, C) → i
13. Segment(C, D) → j
14. Circle(A, (0.15 * i)) → e
15. Intersect(e, h, 1) → E
16. Intersect(e, i, 1) → F
17. CircleSector(A, F, E) → k
18. Polygon(A, C, D) → poly1, d_1, a_1, c_1
19. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'_1
20. Segment(A, A'_1) → l
21. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], C) → A'_2
22. Vector(A, A'_2) → u
23. Translate(k, u) → k'
24. Rotate(k', If[2 < a ≤ 3, (((a - 2) * 2) * π / 3), (2 * π / 3)], C) → k''
25. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], D) → C'_1
26. Vector(C, C'_1) → v
27. Translate(k'', v) → k'''
28. Rotate(k''', If[4 < a ≤ 5, (((a - 4) * 2) * π / 3), (2 * π / 3)], D) → p
29. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], A) → D'
30. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], C) → D'_1
31. Segment(D, D') → m
32. Segment(D, D'_1) → n
33. Rotate(A, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → A'_3
34. Rotate(A'_1, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → G
35. Segment(A'_3, G) → l'
36. Rotate(A, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → A'_4
37. Rotate(A'_1, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → H
38. Segment(A'_4, H) → l'_1