Counter Examples of Congruent Triangles

GeoGebra Commands & Parameters

1. Segment(C, A) → b
2. Angle(A, C, B) → γ_c
3. Segment(B, C) → a_c
4. Segment(A, B) → c_c
5. Angle(B, A, C) → α_c
6. Angle(C, B, A) → β_c
7. Circle(H, c_c) → k_{cSSA}
8. Circle(H, a_c) → p_{aSSA}
9. Point(p_{aSSA}) → I
10. Point(k_{cSSA}) → J
11. Circle(I, b) → q_{bSSA}
12. Segment(H, I) → l
13. Segment(H, J) → m
14. Rotate(H, (-γ_c), I) → H'
15. Angle(H', I, H) → δ
16. Line(H', I) → d
17. Point(d) → D
18. Polygon(C, A, B) → poly1, b_{O}, c_{O}, a_{O}
19. Polygon(H, J, D, I) → poly2_1, h, j, b_{SSAc}, i
20. DynamicCoordinates(D, If[Distance[D, J] < 0.13, x(J), x(D)], If[Distance[D, J] < 0.13, y(J), y(D)]) → E
21. Segment(E, I) → b_{SSA}
22. Polygon(H, I, E) → poly3, e_1, h_1, i_1
23. If(poly1 - 1.5 ≤ poly2_1 ≤ poly1 + 1.5 ∧ E ≟ J, true, false) → g
24. Circle(H_1, c_c) → k_{cSSS}
25. Circle(H_1, a_c) → p_{aSSS}
26. Point(p_{aSSS}) → I_1
27. Point(k_{cSSS}) → J_1
28. Circle(I_1, b) → q_{bSSS}
29. Segment(H_1, I_1) → l_1
30. Segment(H_1, J_1) → m_1
31. Point(q_{bSSS}) → K_1
32. Segment(I_1, K_1) → n_1
33. Segment(B, A) → c
34. Segment(A, C) → b_c
35. Segment(B, C) → a
36. DynamicCoordinates(K_1, If[Distance[J_1, K_1] < 0.13, x(J_1), x(K_1)], If[Distance[K_1, J_1] < 0.13, y(J_1), y(K_1)]) → F
37. Polygon(J_1, H_1, I_1) → poly4, i_2, j_2, h_2
38. Point(p_{aSSS}) → G
39. Segment(H_1, G) → e
40. Rotate(G, β_c, H_1) → G'
41. Angle(G, H_1, G') → α
42. Line(H_1, G') → f
43. Intersect(k_{cSSA}, f, 2) → K
44. Segment(G, L) → k
45. Segment(H_1, K) → n
46. DynamicCoordinates(L, If[Distance[K, L] < 0.13, x(K), x(L)], If[Distance[L, K] < 0.13, y(K), y(L)]) → M
47. Polygon(H_1, G, M) → poly2, m_2, h_3, g_1
48. Point(p_{aSSS}) → N
49. Rotate(N, β_c, H_1) → N'
50. Angle(N, H_1, N') → β
51. Rotate(H_1, α_c, N') → O
52. Line(H_1, N) → p
53. Segment(H_1, N) → s
54. Line(H_1, N') → q
55. Point(q) → P
56. Rotate(H_1, α_c, P) → Q
57. Angle(H_1, P, Q) → γ
58. Line(P, Q) → r
59. Segment(H_1, P) → t
60. Point(r) → R
61. Segment(P, R) → a_1
62. DynamicCoordinates(R, If[Distance[N, R] < 0.13, x(N), x(R)], If[Distance[R, N] < 0.13, y(N), y(R)]) → S
63. Polygon(S, H_1, P) → poly5, p_1, s_1, h_4
64. Point(p_{aSSA}) → T
65. Rotate(T, β_c, H_1) → T'
66. Angle(T, H_1, T') → ε
67. Rotate(H_1, (-γ_c), T) → U
68. Angle(U, T, H_1) → ζ
69. Line(H_1, T') → b_1
70. Line(U, T) → c_1
71. Segment(H_1, T) → d_1
72. Point(c_1) → V
73. Point(b_1) → W
74. DynamicCoordinates(W, If[Distance[V, W] < 0.13, x(V), x(W)], If[Distance[V, W] < 0.13, y(V), y(W)]) → Z
75. Segment(Z, H_1) → f_1
76. Segment(V, T) → k_1
77. Polygon(H_1, V, T) → poly6, t_1, h_5, v
78. Rotate(A_1, β_c, H_1) → B_1
79. Angle(A_1, H_1, B_1) → η
80. Line(H_1, B_1) → r_1
81. Rotate(H_1, (-γ_c), A_1) → C_1
82. Angle(C_1, A_1, H_1) → θ
83. Line(C_1, A_1) → a_2
84. Intersect(r_1, a_2) → D_1
85. Angle(H_1, D_1, A_1) → ι
86. Segment(H_1, A_1) → q_1
87. Segment(D_1, A_1) → b_2
88. Segment(D_1, H_1) → c_2
89. Polygon(A_1, H_1, D_1) → poly7, d_2, a_3, h_6
90. If(a - 0.1 ≤ q_1 ≤ a + 0.1, true, false) → g_2
91. Polygon(H_1, D_1, A_1) → poly8, a_4, h_7, d_3