Investigate Triangle Congruence Theorems

GeoGebra Commands & Parameters

1. Point(Circle[A_{SS}, AB]) → B_{SS}
2. Point(Circle[B_{SS}, BC]) → C_{SS}
3. Polygon(A_{SS}, B_{SS}, C_{SS}) → tri_{SS}, c_{ss}, a_{ss}, b_{ss}
4. Point(Circle[A_{SA}, AB]) → B_{SA}
5. Point(Ray[Rotate[B_{SA}, (-angB), B_{SA}], Rotate[A_{SA}, angB, B_{SA}]]) → C_{SA}
6. Polygon(A_{SA}, B_{SA}, C_{SA}) → tri_{SA}, c_{sa}, a_{sa}, b_{sa}
7. Point(Circle[A_{SSS}, AB]) → B_{SSS}
8. Point(Circle[B_{SSS}, BC]) → C_{SSS}
9. Point(Circle[C_{SSS}, CA]) → AC_{SSS}
10. Segment(A_{SSS}, B_{SSS}) → a
11. Segment(B_{SSS}, C_{SSS}) → b
12. Segment(C_{SSS}, AC_{SSS}) → c
13. Polygon(A_{SSS}, B_{SSS}, C_{SSS}) → tri_{SSS}, c_{sss}, a_{sss}, b_{sss}
14. Point(Circle[A_{SSA}, AB]) → B_{SSA}
15. Point(Circle[B_{SSA}, BC]) → C_{SSA}
16. Point(Ray[Rotate[C_{SSA}, (-angC), C_{SSA}], Rotate[B_{SSA}, angC, C_{SSA}]]) → AC_{SSA}
17. Polygon(A_{SSA}, B_{SSA}, C_{SSA}) → tri_{SSA}, c_{ssa}, a_{ssa}, b_{ssa}
18. Point(Circle[A_{AAS}, CA]) → C_{AAS}
19. Point(Ray[Rotate[A_{AAS}, angA, A_{AAS}], Rotate[C_{AAS}, angA, A_{AAS}]]) → BA_{AAS}
20. Intersect(Ray[Rotate[A_{AAA}, (-angA), A_{AAA}], Rotate[B_{AAA}, (-angA), A_{AAA}]], Ray[Rotate[B_{AAA}, angB, B_{AAA}], Rotate[A_{AAA}, angB, B_{AAA}]]) → C_{AAA}
21. Polygon(A_{AAA}, B_{AAA}, C_{AAA}) → tri_{AAA}, c_{aaa}, a_{aaa}, b_{aaa}
22. Angle(A_{SA}, B_{SA}, C_{SA}) → α
23. Segment(A_{SSA}, B_{SSA}) → d
24. Segment(B_{SSA}, C_{SSA}) → e
25. Segment(C_{SSA}, AC_{SSA}) → f
26. Angle(B_{SSA}, C_{SSA}, AC_{SSA}) → β
27. Segment(A_{AAS}, C_{AAS}) → g
28. Segment(A_{AAS}, BA_{AAS}) → h
29. Angle(C_{AAS}, A_{AAS}, BA_{AAS}) → γ
30. Point(Circle[A_{ASA}, CA]) → C_{ASA}
31. Segment(A_{ASA}, C_{ASA}) → m
32. Point(Ray[Rotate[A_{ASA}, angA, A_{ASA}], Rotate[C_{ASA}, angA, A_{ASA}]]) → BA_{ASA}
33. Segment(A_{ASA}, BA_{ASA}) → n
34. Point(Ray[Rotate[C_{ASA}, (-angC), C_{ASA}], Rotate[A_{ASA}, (-angC), C_{ASA}]]) → BC_{ASA}
35. Segment(C_{ASA}, BC_{ASA}) → p
36. Intersect(Ray[A_{ASA}, BA_{ASA}], Ray[C_{ASA}, BC_{ASA}]) → B_{ASA}
37. Polygon(A_{ASA}, B_{ASA}, C_{ASA}) → tri_{ASA}, c_{asa}, a_{asa}, b_{asa}
38. Angle(BA_{ASA}, A_{ASA}, C_{ASA}) → ζ
39. Angle(BC_{ASA}, C_{ASA}, A_{ASA}) → η
40. Angle(C_{AAA}, B_{AAA}, A_{AAA}) → θ
41. Angle(B_{AAA}, A_{AAA}, C_{AAA}) → ι
42. Angle(A_{AAA}, C_{AAA}, B_{AAA}) → κ
43. Point(Ray[Rotate[BA_{AAS}, angB, BA_{AAS}], Rotate[A_{AAS}, angB, BA_{AAS}]]) → CB_{AAS}
44. Segment(BA_{AAS}, CB_{AAS}) → i
45. Angle(CB_{AAS}, BA_{AAS}, A_{AAS}) → δ
46. Intersect(Ray[Rotate[C_{AAS}, (-angC), C_{AAS}], Rotate[A_{AAS}, (-angC), C_{AAS}]], Ray[Rotate[A_{AAS}, angA, A_{AAS}], Rotate[C_{AAS}, angA, A_{AAS}]]) → B_{AAS}
47. Polygon(A_{AAS}, B_{AAS}, C_{AAS}) → tri_{AAS}, c_{aas}, a_{aas}, b_{aas}
48. Point(Circle[A_{SAS}, AB]) → B_{SAS}
49. Intersect(Circle[A_{SAS}, CA], Ray[Rotate[A_{SAS}, (-angA), A_{SAS}], Rotate[B_{SAS}, (-angA), A_{SAS}]]) → C_{SAS},
50. Polygon(A_{SAS}, B_{SAS}, C_{SAS}) → tri_{SAS}, c_{sas}, a_{sas}, b_{sas}
51. Angle(C_{SAS}, A_{SAS}, B_{SAS}) → ε
52. Point(Circle[A_1, AB]) → B_1
53. Point(Ray[Rotate[B_1, (-angB), B_1], Rotate[A_1, angB, B_1]]) → C_1
54. Polygon(A_1, B_1, C_1) → tri_1, c_{sa1}, a_{sa1}, b_{sa1}
55. Angle(A_1, B_1, C_1) → α_1
56. LaTeX(c_{sa}, true, true) → text1
57. Point(Circle[A_2, AB]) → B_2
58. Point(Circle[B_2, BC]) → C_2
59. Segment(A_2, B_2) → a_2
60. Segment(B_2, C_2) → b_2
61. Polygon(A_2, B_2, C_2) → tri_2, c_1, a_1, b_1
62. Point(Circle[A_3, CA]) → C_3
63. Segment(A_3, C_3) → g_1
64. Intersect(Ray[Rotate[C_3, (-angC_1), C_3], Rotate[A_3, (-angC_1), C_3]], Ray[Rotate[A_3, angA, A_3], Rotate[C_3, angA, A_3]]) → B_3
65. Polygon(A_3, B_3, C_3) → tri_3, c_2, a_3, b_3
66. Point(Circle[A_4, AB]) → B_4
67. Intersect(Circle[A_4, CA], Ray[Rotate[A_4, (-angA), A_4], Rotate[B_4, (-angA), A_4]]) → C_4,
68. Polygon(A_4, B_4, C_4) → tri_4, c_3, a_4, b_4
69. Angle(C_4, A_4, B_4) → ε_1
70. Intersect(Ray[Rotate[A_5, (-angA), A_5], Rotate[B_5, (-angA), A_5]], Ray[Rotate[B_5, angB, B_5], Rotate[A_5, angB, B_5]]) → C_5
71. Polygon(A_5, B_5, C_5) → tri_5, c_4, a_5, b_5
72. Angle(C_5, B_5, A_5) → θ_1
73. Angle(B_5, A_5, C_5) → ι_1
74. Angle(A_5, C_5, B_5) → κ_1
75. Point(Circle[A_6, AB]) → B_6
76. Point(Circle[B_6, BC]) → C_6
77. Polygon(A_6, B_6, C_6) → tri_6, c_5, a_6, b_6
78. Point(Circle[A_7, AB]) → B_7
79. Point(Circle[B_7, BC]) → C_7
80. Polygon(A_7, B_7, C_7) → tri_7, c_6, a_7, b_7
81. Segment(A_7, B_7) → d_1
82. Segment(B_7, C_7) → e_1
83. Point(Circle[A_8, CA]) → C_8
84. Segment(A_8, C_8) → m_1
85. Point(Ray[Rotate[A_8, angA, A_8], Rotate[C_8, angA, A_8]]) → BA_1
86. Segment(A_8, BA_1) → n_1
87. Point(Ray[Rotate[C_8, (-angC_4), C_8], Rotate[A_8, (-angC_4), C_8]]) → BC_1
88. Segment(C_8, BC_1) → p_1
89. Intersect(Ray[A_8, BA_1], Ray[C_8, BC_1]) → B_8
90. Polygon(A_8, B_8, C_8) → tri_8, c_7, a_8, b_8
91. Angle(BA_1, A_8, C_8) → ζ_1
92. Angle(BC_1, C_8, A_8) → η_1
93. Point(Circle[A_9, CA_1]) → C_9
94. Segment(A_9, C_9) → m_2
95. Point(Ray[Rotate[A_9, angA_1, A_9], Rotate[C_9, angA_1, A_9]]) → BA_2
96. Segment(A_9, BA_2) → n_2
97. Point(Ray[Rotate[C_9, (-angC_8), C_9], Rotate[A_9, (-angC_8), C_9]]) → BC_2
98. Segment(C_9, BC_2) → p_2
99. Intersect(Ray[A_9, BA_2], Ray[C_9, BC_2]) → B_9
100. Polygon(A_9, B_9, C_9) → tri_9, c_8, a_9, b_9
101. Angle(BA_2, A_9, C_9) → ζ_2
102. Angle(BC_2, C_9, A_9) → η_2