GeoGebra Geometric Construction: Triangle Symmetry and Median Line

GeoGebra Commands & Parameters

1. Point(Ray[A, A + (1, 0)]) → B
2. PointIn(d) → C
3. Polygon(A, B, C) → t1, f, a, b
4. OrthogonalLine(C, g) → h
5. Intersect(g, h) → C_{1}
6. Midpoint(C, C_{1}) → D
7. Midpoint(b) → E
8. Midpoint(a) → G
9. Dilate(C, If[0 < c ≤ 1, 1 - c, 0], D) → F'
10. Segment(C, F') → i
11. Dilate(D, If[1 < c ≤ 2, 2 - c, 0], C_{1}) → D'
12. Segment(D, D') → j
13. Rotate(C, If[2 < c ≤ 3, ((c - 2) * pi), pi], D) → F'_{1}
14. Rotate(F', If[2 < c ≤ 3, ((c - 2) * pi), pi], D) → F''
15. Segment(F'_{1}, F'') → i'
16. Dilate(E, If[0 < c ≤ 2, (0.5 * (2 - c)), 0], D) → E'
17. Segment(E, E') → k
18. Dilate(G, If[0 < c ≤ 2, (0.5 * (2 - c)), 0], D) → G'
19. Segment(G, G') → l
20. Angle(C, B, A) → β
21. Angle(B, A, C) → γ
22. Polygon(A, B, G, E) → q1, a_1, b_1, g_1, e
23. Polygon(G, C, E) → t2, e_1, g_2, f_1
24. Rotate(G, If[4 < c ≤ 5, ((c - 4) * pi), pi], E) → G'_{1}
25. Rotate(C, If[4 < c ≤ 5, ((c - 4) * pi), pi], E) → F'_{2}
26. Rotate(E, If[4 < c ≤ 5, ((c - 4) * pi), pi], E) → E'_{1}
27. Polygon(G'_{1}, F'_{2}, E'_{1}) → t2', e'_{1}, g'_{1}, f'_{2}
28. Segment(A, E) → m
29. Segment(B, G) → n
30. Segment(G, C) → p
31. Segment(C, E) → q
32. Segment(F'_{2}, E) → r
33. Segment(E, G'_{1}) → s
34. Segment(G'_{1}, F'_{2}) → t
35. Segment(G, C) → h_1
36. Segment(C, E) → i_1
37. If(β ≟ pi / 2, 5, 8) → o
38. OrthogonalLine(B, p_1) → j_1
39. Intersect(p_1, j_1) → H
40. OrthogonalLine(G, g) → k_1
41. Intersect(k_1, g) → I
42. Dilate(G, If[5 < c ≤ 6, 6 - c, 0], I) → G'_{2}
43. Segment(G, G'_{2}) → l_1
44. Polygon(A, I, G, G'_{1}) → q2, a_2, i_2, g_3, m_1
45. Polygon(I, B, G) → t3, g_4, i_3, b_2
46. Dilate(G, If[7 < c ≤ 8, 8 - c, 0], G'_{1}) → G'_{3}
47. Vector(G, G'_{3}) → u
48. Translate(I, u) → I'
49. Translate(B, u) → B'
50. Translate(G, u) → G'_{4}
51. Polygon(I', B', G'_{4}) → t3', g'_{4}, n_1, b'
52. Segment(G'_{3}, I') → q_1
53. Segment(G'_{3}, B') → r_1
54. Dilate(B, If[5 < c ≤ 6, 6 - c, 0], H) → H'
55. Polygon(A, B, H, G'_{1}) → q3, a_3, b_3, h_2, t_1
56. Polygon(B, H, G) → t4, g_5, b_4, h_3
57. Translate(B, u) → B'_{1}
58. Translate(H, u) → H'_{1}
59. Translate(G, u) → G'_{5}
60. Polygon(B'_{1}, H'_{1}, G'_{5}) → t4', g'_{5}, b'_{1}, h'_{1}
61. Segment(B'_{1}, G'_{3}) → c_1
62. Segment(B'_{1}, H'_{1}) → d_1
63. Segment(B, H') → s_1
64. Point(Line[A, B]) → F
65. Point(f_2) → J
66. Intersect(eq1, Line[A, B]) → K
67. Segment(J, K) → j_2
68. Point(Line[A, B]) → L
69. Angle(L, K, J) → α
70. Angle(K, J, C) → δ
71. RotateText(text2, pi / 2) → text3