Haga's Theorem Demonstration

GeoGebra Commands & Parameters

1. Point(xAxis) → C
2. Point(yAxis) → B
3. Polygon(B, C, 4) → poly1, a, b, c, d, D, A
4. Point(c) → E
5. Segment(E, C) → l
6. Vector(C, E) → u
7. Point(l) → CC
8. Midpoint(CC, C) → C1
9. OrthogonalLine(C1, u, xOyPlane) → e
10. Intersect(a, e) → M
11. Intersect(b, e) → F
12. Polygon(M, CC, F) → poly2, i, h, f
13. Mirror(M, e) → H'
14. Mirror(CC, e) → F'
15. Mirror(F, e) → I'
16. Polygon(H', F', I') → poly2', i', h', f'
17. Intersect(e, d) → J
18. Polygon(B, J, I', C) → poly3, a_1, j, i'_{1}, b_1
19. Mirror(B, e) → I
20. Mirror(J, e) → G
21. Mirror(I', e) → I''
22. Mirror(C, e) → B'
23. Polygon(I, G, I'', B') → poly3', a', j', i'', b'
24. Intersect(b', d) → H
25. Polygon(G, I, H) → poly4, f_1, j'_1, a'_1
26. Polygon(H, A, E) → poly5, e_1, f_2, d_1
27. Polygon(E, D, F) → poly6, i_1, e_2, c_1
28. Vector(A, O) → v
29. Intersect(d, b') → Q
30. Vector(Q, P) → w
31. Vector(E, R) → n
32. Translate(A, Vector[(Controle / 5 * v)]) → A'
33. Translate(E, Vector[(Controle / 5 * n)]) → E'
34. Translate(H, Vector[(Controle / 5 * w)]) → H'_{1}
35. Angle(E', A', H'_{1}, xOyPlane) → κ
36. Vector(D, O) → q
37. Translate(D, Vector[(Controle / 5 * q)]) → D'
38. Vector(I'', S) → r
39. Vector(E, T) → s
40. Translate(I'', Vector[(Controle / 5 * r)]) → I'''
41. Translate(E, Vector[(Controle / 5 * s)]) → E'_{1}
42. Polygon(A', E', H'_{1}) → t1, h'_{1}, p, e'
43. Polygon(I''', D', E'_{1}) → t2, e'_{1}, i''', d'
44. Intersect(a', b') → U
45. Vector(H, V) → v_1
46. Translate(H, Vector[(Controle / 5 * v_1)]) → H'_{2}
47. Vector(J, W) → w_1
48. Vector(I, O) → u_1
49. Translate(I, Vector[(Controle / 5 * u_1)]) → I'_{1}
50. Translate(J, Vector[(Controle / 5 * w_1)]) → J'
51. Polygon(H'_{2}, I'_{1}, J') → t3, g_1, h'_{2}, i'_{2}
52. Polygon(CC, I'', H') → t4, h_1, j_1, k_1
53. Segment(CC, I') → g