Dynamic Demonstration of Triangle Angle Trisectors

GeoGebra Commands & Parameters

1. Rotate(A, (-((a * π / 180))), B) → A'
2. Angle(A', B, A) → α
3. Segment(A, B) → f
4. Ray(B, A') → g
5. Point(g) → C
6. Segment(A, C) → h
7. Segment(B, C) → i
8. LineBisector(i) → j
9. LineBisector(f) → k
10. Line(A, B) → m
11. OrthogonalLine(C, m) → n
12. Intersect(m, n) → E
13. Angle(E, C, A) → γ
14. Angle(E, A, C) → ε
15. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], E) → C'_1
16. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], E) → B'
17. Midpoint(A, B) → J
18. Segment(A, E) → g_1
19. Segment(A, J) → h_1
20. Min(f, i) → u
21. Circle(B, (0.2 * u)) → r_1
22. Intersect(r_1, f) → K,
23. Intersect(r_1, i) → L,
24. CircleSector(B, L, K) → s_1
25. Point(f) → M
26. Segment(C, M) → p
27. Line(C, M) → q
28. OrthogonalLine(A, q) → r
29. Line(C, B) → s
30. OrthogonalLine(A, s) → c
31. Angle(A, C, M) → θ
32. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], M) → C'_2
33. Angle(A, C, B) → κ_2
34. Polygon(A, B, C) → poly1, c_2, a_1, b
35. Circle(B, 1) → d
36. Circle(C, 1) → t_1
37. Intersect(d, s) → D, F
38. Intersect(t_1, s) → G, H
39. Angle(C, B, A) → δ
40. Rotate(C, δ / 3, B) → C'
41. Angle(C, B, C') → κ
42. Rotate(C', κ, B) → C''
43. Angle(C', B, C'') → η
44. Line(B, C') → f_2
45. Line(B, C'') → g_2
46. Circle(C, h / 3) → d_2
47. Intersect(d_2, h) → I,
48. Circle(I, h / 3) → e_2
49. Intersect(e_2, h) → S, T
50. Intersect(f_2, h) → U
51. Intersect(g_2, h) → V
52. Intersect(r_1, f_2, 2) → W
53. Intersect(r_1, g_2) → Z, A_1
54. CircleSector(B, L, W) → h_2
55. Polygon(C, U, B) → poly2, b_2, c_3, u_1
56. Polygon(U, B, V) → poly3, v_1, u_2, b_3
57. Polygon(V, B, A) → poly4, a_2, v_2, b_4
58. Line(C, A) → i_2
59. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], I) → C'_3
60. Segment(C, C'_3) → t
61. Rotate(C, If[1 < o ≤ 2, ((o - 1) * π), π], I) → C'_4
62. Rotate(C'_3, If[1 < o ≤ 2, ((o - 1) * π), π], I) → N
63. Segment(C'_4, N) → t'
64. Polygon(U, V, B) → poly5, b_5, u_3, v
65. Rotate(C'_4, If[2 < o ≤ 3, ((o - 2) * π), π], S) → P
66. Rotate(N, If[2 < o ≤ 3, ((o - 2) * π), π], S) → N'
67. Segment(P, N') → t''
68. Dilate(B, If[3.5 < o ≤ 4.5, 4.5 - o, 0], U) → B'_1
69. Dilate(B, If[3.5 < o ≤ 4.5, 4.5 - o, 0], V) → B'_2
70. Segment(B, B'_1) → l
71. Segment(B, B'_2) → e
72. Polygon(U, V, B) → poly6, b_1, u_4, v_3
73. Rotate(h_2, If[5 < o ≤ 6, ((o - 5) * κ), κ], B) → c_1
74. Rotate(c_1, If[6.5 < o ≤ 7.5, ((o - 6.5) * κ), κ], B) → d_1
75. Dilate(U, If[7.5 < o ≤ 8.5, 8.5 - o, 0], V) → U'
76. Segment(U, U') → f_1
77. Dilate(V, If[9 < o ≤ 10, 10 - o, 0], I) → V'
78. Vector(V, V') → w
79. Translate(U, w) → U'_1
80. Polygon(U'_1, V', B) → poly7, b_6, u'_1, v'
81. Segment(U'_1, V') → i_1
82. Segment(B, U'_1) → j_1
83. Segment(B, I) → k_1
84. Polygon(V, V', B) → poly8, b_7, v_4, v'_1
85. Segment(B, V') → l_1
86. Polygon(V', B, V) → poly9, v_5, v'_2, b_8