Sallows' Theorem: Triangle Medians

GeoGebra Commands & Parameters

1. Polygon(A, B, C) → t1, c, a_1, b
2. Midpoint(b) → D
3. Midpoint(a_1) → E
4. Midpoint(c) → F
5. Segment(A, E) → f
6. Segment(B, D) → g
7. Segment(C, F) → h
8. Intersect(f, h) → G
9. Polygon(A, F, G) → t2, g_1, a_2, f_1
10. Polygon(F, B, G) → t3, g_2, f_2, b_1
11. Polygon(A, G, D) → t4, d, a_3, g_3
12. Polygon(G, D, C) → t5, c_1, g_4, d_1
13. Polygon(G, B, E) → t6, e, g_5, b_2
14. Polygon(G, E, C) → t7, c_2, g_6, e_1
15. Vector(A, G) → u
16. Vector(C, G) → v
17. Vector(B, G) → w
18. Min(1, Max[0, A1]) → A2
19. Min(1, Max[0, A1 - 2.2]) → A4
20. Min(1, Max[0, A1 - 1.1]) → A3
21. Translate(A, C2) → A'
22. Translate(G, C2) → G'
23. Translate(D, C2) → D'
24. Polygon(A', G', D') → t4', d', a', g'
25. Translate(G, C2) → G'_1
26. Translate(D, C2) → D'_1
27. Translate(C, C2) → C'
28. Polygon(G'_1, D'_1, C') → t5', c', g'_1, d'_1
29. Translate(G, B2) → G'_2
30. Translate(E, B2) → E'
31. Translate(C, B2) → C'_1
32. Polygon(G'_2, E', C'_1) → t7', c'_1, g'_2, e'
33. Translate(G, B2) → G'_3
34. Translate(B, B2) → B'
35. Translate(E, B2) → E'_1
36. Polygon(G'_3, B', E'_1) → t6', e'_1, g'_3, b'
37. Translate(F, D2) → F'
38. Translate(B, D2) → B'_1
39. Translate(G, D2) → G'_4
40. Polygon(F', B'_1, G'_4) → t3', g'_4, f', b'_1
41. Translate(A, D2) → A'_1
42. Translate(F, D2) → F'_1
43. Translate(G, D2) → G'_5
44. Polygon(A'_1, F'_1, G'_5) → t2', g'_5, a'_1, f'_1
45. Rotate(A', (-((A3 * 90°))), D') → A''
46. Rotate(G', (-((A3 * 90°))), D') → G''
47. Rotate(D', (-((A3 * 90°))), D') → D''
48. Polygon(A'', G'', D'') → t4'', d'', a'', g''
49. Rotate(G'_1, (A3 * 90°), D') → H
50. Rotate(D'_1, (A3 * 90°), D') → I
51. Rotate(C', (A3 * 90°), D') → C''
52. Polygon(H, I, C'') → t5'', c'', h_1, i
53. Rotate(A'_1, (A3 * 90°), F') → J
54. Rotate(F'_1, (A3 * 90°), F') → K
55. Rotate(G'_5, (A3 * 90°), F') → L
56. Polygon(J, K, L) → t2'', l, j, k
57. Rotate(F', (-((A3 * 90°))), F') → F''
58. Rotate(B'_1, (-((A3 * 90°))), F') → M
59. Rotate(G'_4, (-((A3 * 90°))), F') → N
60. Polygon(F'', M, N) → t3'', n, f'', m
61. Rotate(G'_2, (-((A3 * 90°))), E') → O
62. Rotate(E', (-((A3 * 90°))), E') → E''
63. Rotate(C'_1, (-((A3 * 90°))), E') → P
64. Polygon(O, E'', P) → t7'', p, o, e''
65. Rotate(G'_3, (A3 * 90°), E') → Q
66. Rotate(B', (A3 * 90°), E') → B''
67. Rotate(E'_1, (A3 * 90°), E') → R
68. Polygon(Q, B'', R) → t6'', r, q, b''
69. Translate(J, D4) → J'
70. Translate(K, D4) → K'
71. Translate(L, D4) → L'
72. Polygon(J', K', L') → t2''', l', j', k'
73. Translate(F'', D4) → F'''
74. Translate(M, D4) → M'
75. Translate(N, D4) → N'
76. Polygon(F''', M', N') → t3''', n', f''', m'
77. Translate(A'', C4) → A'''
78. Translate(G'', C4) → G'''
79. Translate(D'', C4) → D'''
80. Polygon(A''', G''', D''') → t4''', d''', a''', g'''
81. Translate(H, C4) → H'
82. Translate(I, C4) → I'
83. Translate(C'', C4) → C'''
84. Polygon(H', I', C''') → t5''', c''', h', i'
85. Translate(Q, B4) → Q'
86. Translate(B'', B4) → B'''
87. Translate(R, B4) → R'
88. Polygon(Q', B''', R') → t6''', r', q', b'''
89. Translate(O, B4) → O'
90. Translate(E'', B4) → E'''
91. Translate(P, B4) → P'
92. Polygon(O', E''', P') → t7''', p', o', e'''
93. Angle(J', L', K') → α
94. Angle(P', O', E''') → β
95. Angle(D''', G''', A''') → δ
96. Angle(C''', H', D''') → γ
97. Angle(B''', Q', R') → ε
98. Angle(F''', N', M') → ζ
99. Angle(Q', B''', R') → η
100. Angle(E''', P', O') → θ
101. Angle(F''', M', N') → ι
102. Angle(K', J', L') → κ
103. Angle(D''', A''', G''') → λ
104. Angle(H', C''', I') → μ