Conditions for Triangles to be Congruent

GeoGebra Commands & Parameters

1. Segment(A_1, B_1) → a_1
2. Circle(A_1, B_1) → circle1_1
3. Circle(C_1, B_1) → circle1_2
4. Segment(B_1, C_1) → b_1
5. Segment(C_1, A_1) → c_1
6. Point(Circle[E_1, abs(a_1)]) → D_1
7. Circle(D_1, c_1) → circle1_3
8. Circle(E_1, b_1) → circle1_4
9. Intersect(circle1_3, circle1_4, 1) → F_1
10. Segment(D_1, E_1) → d_1
11. Segment(E_1, F_1) → e_1
12. Segment(D_1, F_1) → f_1
13. Polygon(A_1, B_1, C_1) → poly1_1, mc_1, ma_1, mb_1
14. Polygon(D_1, E_1, F_1) → poly1_2, mf_1, md_1, me_1
15. Circle(B_2, A_2) → circle2_1
16. Circle(B_2, C_2) → circle2_2
17. Segment(A_2, B_2) → a_2
18. Segment(B_2, C_2) → b_2
19. Segment(A_2, C_2) → c_2
20. Angle(C_2, B_2, A_2) → α_21
21. Circle(E_2, a_2) → circle2_3
22. Circle(E_2, b_2) → circle2_4
23. Point(circle2_3) → D_2
24. Rotate(D_2, (-α_21), E_2) → E_2'
25. Line(E_2, E_2') → line2'
26. Intersect(circle2_4, line2', 2) → F_2
27. Segment(D_2, E_2) → d_2
28. Segment(E_2, F_2) → e_2
29. Segment(D_2, F_2) → f_2
30. Angle(F_2, E_2, D_2) → α_22
31. Polygon(A_2, B_2, C_2) → poly2_1, mc_2, ma_2, mb_2
32. Polygon(D_2, E_2, F_2) → poly2_2, mf_2, md_2, me_2
33. Segment(B_{34}, C_{34}) → b_{34}
34. Circle(B_{34}, C_{34}) → circle34_1
35. Segment(B_{34}, A_{34}) → a_{34}
36. Segment(C_{34}, A_{34}) → c_{34}
37. Angle(C_{34}, B_{34}, A_{34}) → α_31
38. Angle(B_{34}, C_{34}, A_{34}) → β_31
39. Circle(E_{34}, b_{34}) → circle34_2
40. Point(circle34_2) → F_{34}
41. Rotate(F_{34}, α_31, E_{34}) → F_{34}'
42. Rotate(E_{34}, (-β_31), F_{34}) → E_{34}'
43. Line(E_{34}, F_{34}') → line34_1'
44. Line(F_{34}, E_{34}') → line34_2'
45. Intersect(line34_1', line34_2') → D_{34}
46. Segment(D_{34}, E_{34}) → d_{34}
47. Segment(E_{34}, F_{34}) → e_{34}
48. Segment(D_{34}, F_{34}) → f_{34}
49. Angle(F_{34}, E_{34}, D_{34}) → α_32
50. Angle(D_{34}, F_{34}, E_{34}) → β_32
51. Polygon(A_{34}, B_{34}, C_{34}) → poly34_1, ma_3, mb_3, mc_3
52. Polygon(D_{34}, E_{34}, F_{34}) → poly34_2, md_3, me_3, mf_3
53. Angle(C_{34}, A_{34}, B_{34}) → β_41
54. Angle(F_{34}, D_{34}, E_{34}) → β_42
55. Segment(A_5, C_5) → c_5
56. OrthogonalLine(C_5, c_5) → line5_1'
57. Point(line5_1') → B_5
58. Segment(A_5, B_5) → a_5
59. Segment(B_5, C_5) → b_5
60. Circle(D_5, c_5) → circle5_1
61. Point(circle5_1) → F_5
62. Segment(D_5, F_5) → f_5
63. OrthogonalLine(F_5, f_5) → line5_2'
64. Circle(D_5, a_5) → circle5_2
65. Intersect(circle5_2, line5_2', 1) → E_5
66. Segment(D_5, E_5) → d_5
67. Segment(E_5, F_5) → e_5
68. Angle(A_5, C_5, B_5) → α_51
69. Angle(D_5, F_5, E_5) → α_52
70. Polygon(A_5, B_5, C_5) → poly5_1, mc_5, ma_5, mb_5
71. Polygon(D_5, E_5, F_5) → poly5_2, mf_5, md_5, me_5
72. Segment(A_6, B_6) → a_6
73. Circle(B_6, A_6) → circle6_1
74. Circle(A_6, C_6) → circle6_2
75. Segment(B_6, C_6) → b_6
76. Segment(A_6, C_6) → c_6
77. Circle(D_6, a_6) → circle6_3
78. Point(circle6_3) → E_6
79. Circle(D_6, c_6) → circle6_4
80. Angle(C_6, B_6, A_6) → α_61
81. Rotate(D_6, (-α_61), E_6) → F_6'
82. Line(E_6, F_6') → line6'
83. Intersect(circle6_4, line6', 1) → F_6
84. Segment(D_6, E_6) → d_6
85. Segment(E_6, F_6) → e_6
86. Segment(D_6, F_6) → f_6
87. Angle(F_6, E_6, D_6) → α_62
88. Polygon(A_6, B_6, C_6) → poly6_1, mc_6, ma_6, mb_6
89. Polygon(D_6, E_6, F_6) → poly6_2, mf_6, md_6, me_6
90. Segment(A_7, B_7) → a_7
91. Segment(B_7, C_7) → b_7
92. Segment(A_7, C_7) → c_7
93. Segment(D_7, E_7) → d_7
94. Angle(C_7, A_7, B_7) → α_71
95. Angle(A_7, B_7, C_7) → β_71
96. Angle(B_7, C_7, A_7) → γ_71
97. Rotate(E_7, (-α_71), D_7) → F_71'
98. Rotate(D_7, β_71, E_7) → F_72'
99. Line(D_7, F_71') → line7_1'
100. Line(E_7, F_72') → line7_2'
101. Intersect(line7_1', line7_2') → F_7
102. Segment(D_7, F_7) → e_7
103. Segment(E_7, F_7) → f_7
104. Angle(F_7, D_7, E_7) → α_72
105. Angle(D_7, E_7, F_7) → β_72
106. Angle(E_7, F_7, D_7) → γ_72
107. Polygon(A_7, B_7, C_7) → poly7_1, mc_7, ma_7, mb_7
108. Polygon(D_7, E_7, F_7) → poly7_2, mf_7, md_7, me_7