Dynamic Proof of SAS Triangle Congruence Theorem by Aaron Dankman

GeoGebra Commands & Parameters

1. Circle(A, a) → c
2. Point(c) → B
3. Segment(A, B) → f
4. Circle(A, b) → d
5. Rotate(B, α, A) → B'
6. Angle(B, A, B') → β
7. Ray(A, B') → g
8. Intersect(d, g, 1) → C
9. Segment(B, C) → h
10. Segment(A, C) → i
11. Min(f, i) → e
12. Circle(A, (0.25 * e)) → k
13. Intersect(k, f) → D,
14. Intersect(k, i) → E,
15. Polygon(A, B, C) → poly1, c_1, a_1, b_1
16. CircleSector(A, D, E) → p
17. Mirror(A, h) → A'
18. Mirror(B, h) → B'_1
19. Mirror(C, h) → C'
20. Polygon(A', B'_1, C') → poly1', c', a', b'_1
21. Mirror(p, h) → p'
22. Mirror(A, h) → A'_1
23. Mirror(B, h) → B'_2
24. Segment(A'_1, B'_2) → f'
25. Mirror(A, h) → A'_2
26. Mirror(C, h) → C'_1
27. Segment(A'_2, C'_1) → i'
28. Line(C, B) → j
29. Point(j) → G
30. Point(j) → H
31. Ray(B, H) → l
32. Ray(C, G) → m
33. Circle(F, a) → q
34. Point(q) → I
35. Segment(F, I) → n
36. Rotate(I, α, F) → I'
37. Angle(I, F, I') → γ
38. Circle(F, b) → r
39. Ray(F, I') → s
40. Intersect(r, s, 1) → J
41. Segment(I, J) → t
42. Segment(F, J) → f_1
43. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], I) → B'_3
44. Vector(B, B'_3) → v
45. Translate(A, v) → A'_3
46. Translate(B, v) → B'_4
47. Segment(A'_3, B'_4) → f'_1
48. Line(B, n) → g_1
49. Point(g_1) → K
50. Angle(K, B, A) → δ
51. Rotate(A'_3, If[1 < u ≤ 2, ((-(u - 1)) * δ), (-δ)], I) → L
52. Rotate(B'_4, If[1 < u ≤ 2, ((-(u - 1)) * δ), (-δ)], I) → M
53. Segment(L, M) → h_1
54. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], F) → A'_4
55. Vector(A, A'_4) → w
56. Translate(A, w) → A'_5
57. Translate(C, w) → C'_2
58. Segment(A'_5, C'_2) → i'_1
59. Line(A, f_1) → i_1
60. Point(i_1) → N
61. Angle(N, A, C) → ε
62. Rotate(A'_5, If[3 < u ≤ 4, ((-(u - 3)) * ε), (-ε)], F) → O
63. Rotate(C'_2, If[3 < u ≤ 4, ((-(u - 3)) * ε), (-ε)], F) → P
64. Segment(O, P) → j_1
65. Translate(p, w) → p'_1
66. Rotate(p'_1, If[3 < u ≤ 4, ((-(u - 3)) * ε), (-ε)], F) → d_1
67. Dilate(B, If[4 < u ≤ 5, 5 - u, 0], I) → B'_5
68. Vector(B, B'_5) → u_1
69. Translate(A, u_1) → A'_6
70. Translate(B, u_1) → B'_6
71. Translate(C, u_1) → C'_3
72. Polygon(A'_6, B'_6, C'_3) → poly1'_1, c'_3, a'_6, b'_6
73. Line(B, t) → k_1
74. Point(k_1) → Q
75. Angle(Q, B, C) → ζ
76. Rotate(A'_6, If[5 < u ≤ 6, ((-(u - 5)) * ε), (-ε)], I) → R
77. Rotate(B'_6, If[5 < u ≤ 6, ((-(u - 5)) * ε), (-ε)], I) → S
78. Rotate(C'_3, If[5 < u ≤ 6, ((-(u - 5)) * ε), (-ε)], I) → T
79. Polygon(R, S, T) → poly2, t_1, r_1, s_1
80. Segment(B, A) → l_1
81. Segment(A, C) → m_1
82. Segment(C, B) → n_1
83. CircleSector(A, D, E) → e_1