Dynamic Demonstration of Triangle Medians

GeoGebra Commands & Parameters

1. Midpoint(A, C) → M_B
2. Segment(M_B, C) → j_3
3. Segment(A, M_B) → i_3
4. Rotate(C, (a * π / 180), A) → C'
5. Ray(A, C') → g
6. Point(g) → B
7. Midpoint(A, B) → M_C
8. Segment(M_C, A) → q_3
9. Segment(B, M_C) → n_3
10. Midpoint(C, B) → M_A
11. Segment(M_A, B) → m_3
12. Segment(C, M_A) → l_3
13. Segment(A, C) → f
14. Angle(C, A, C') → α
15. Segment(C, B) → h
16. Ray(M_B, M_A) → i
17. Line(A, C) → j
18. Line(B, j) → k
19. Intersect(k, i) → D
20. Polygon(A, B, C) → poly1, c, a_1, b
21. Polygon(M_C, D, C) → poly2, c_1, m_c, d
22. Segment(B, M_B) → l
23. Segment(C, D) → m
24. Segment(A, C) → n
25. Segment(A, M_A) → p
26. Segment(M_C, D) → q
27. Segment(M_A, D) → r
28. Segment(A, B) → s
29. Intersect(q, h) → E
30. OrthogonalLine(M_A, m) → t
31. Intersect(l, p) → G
32. OrthogonalLine(G, n) → f_1
33. Segment(D, M_B) → g_1
34. Dilate(A, If[0 < v ≤ 1, 1 - v, 0], M_B) → A'
35. Dilate(C, If[0 < v ≤ 1, 1 - v, 0], M_A) → C'_1
36. Segment(A, A') → h_1
37. Segment(C, C'_1) → i_1
38. Dilate(B, If[0 < v ≤ 1, 1 - v, 0], M_C) → B'
39. Segment(B, B') → j_1
40. Rotate(A, If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_B) → A'_1
41. Rotate(A', If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_B) → A''
42. Segment(A'_1, A'') → k_1
43. Rotate(C, If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_A) → C'_2
44. Rotate(C'_1, If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_A) → F
45. Segment(C'_2, F) → l_1
46. Rotate(B, If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_C) → B'_1
47. Rotate(B', If[1 < v ≤ 2, ((-(v - 1)) * π), (-π)], M_C) → B''
48. Segment(B'_1, B'') → m_1
49. Min({i_3, j_3, l_3, m_3, n_3, q_3}) → w
50. Circle(A, (0.25 * w)) → d_1
51. Intersect(d_1, j) → I, J
52. Circle(C, (0.25 * w)) → e_1
53. Intersect(e_1, j) → K, L
54. Intersect(d_1, g) → M,
55. CircleSector(A, J, M) → p_1
56. Line(D, C) → n_1
57. Intersect(e_1, n_1) → N, O
58. Angle(L, C, N) → β
59. Line(M_C, D) → q_1
60. Line(A, M_A) → r_1
61. Line(D, M_A) → s_1
62. Circle(D, (0.25 * w)) → t_1
63. Intersect(t_1, q_1) → R, S
64. Intersect(t_1, s_1) → T, U
65. CircleSector(D, R, U) → c_2
66. Dilate(B, If[2 < v ≤ 3, 3 - v, 0], M_B) → B'_2
67. Dilate(A, If[2 < v ≤ 3, 3 - v, 0], M_A) → A'_2
68. Dilate(C, If[2 < v ≤ 3, 3 - v, 0], M_C) → C'_3
69. Segment(B, B'_2) → b_1
70. Segment(A, A'_2) → f_2
71. Segment(C, C'_3) → g_2
72. Circle(B, 1) → d_2
73. Intersect(d_2, g, 2) → H
74. Ray(B, H) → h_2
75. Dilate(M_C, If[6 < v ≤ 7, 7 - v, 0], D) → P
76. Dilate(B, If[4 < v ≤ 5, 5 - v, 0], D) → B'_3
77. Ray(B, D) → i_2
78. Circle(D, 1) → e_2
79. Intersect(e_2, i_2, 2) → Q
80. Ray(D, Q) → j_2
81. Segment(B, B'_3) → k_2
82. Segment(M_C, P) → l_2
83. Dilate(M_B, If[3 < v ≤ 4, 4 - v, 0], M_A) → V
84. Segment(M_B, V) → m_2
85. Dilate(M_A, If[4 < v ≤ 5, 5 - v, 0], D) → W
86. Segment(M_A, W) → n_2
87. Dilate(A, If[5 < v ≤ 6, 6 - v, 0], B) → A'_3
88. Vector(A, A'_3) → u_1
89. Translate(p_1, u_1) → p_2
90. Ray(C, L) → q_2
91. Dilate(C, If[6 < v ≤ 7, 7 - v, 0], D) → C'_4
92. Segment(C, C'_4) → r_2
93. Ray(M_B, D) → s_2
94. Circle(D, 1) → t_2
95. Intersect(t_2, s_2) → Z, A_1
96. Ray(D, A_1) → a_2
97. Ray(D, M_C) → b_2
98. Circle(M_C, 1) → c_3
99. Intersect(c_3, b_2, 2) → B_1
100. Ray(M_C, B_1) → f_3
101. Dilate(B, If[8 < v ≤ 9, 9 - v, 0], D) → B'_4
102. Vector(B, B'_4) → v_1
103. Translate(p_2, v_1) → d_3
104. Rotate(L, If[9 < v ≤ 10, ((v - 9) * β), β], C) → L'
105. CircleSector(C, L, L') → e_3
106. Dilate(C, If[10 < v ≤ 11, 11 - v, 0], M_B) → C'_5
107. Vector(C, C'_5) → w_1
108. Translate(e_3, w_1) → g_3
109. Angle(R, D, U) → γ
110. Rotate(R, If[11 < v ≤ 12, ((v - 11) * γ), γ], D) → R'
111. CircleSector(D, R, R') → h_3
112. Dilate(D, If[12 < v ≤ 13, 13 - v, 0], M_C) → D'
113. Dilate(D, If[13 < v ≤ 14, 14 - v, 0], M_A) → D'_1
114. Vector(D, D') → u_2
115. Translate(h_3, u_2) → k_3
116. Vector(D, D'_1) → v_2
117. Translate(h_3, v_2) → p_3