Quadrilaterals and Rotational Symmetry

GeoGebra Commands & Parameters

1. Segment(A, B) → a
2. OrthogonalLine(A, a) → b
3. OrthogonalLine(B, a) → c
4. Point(b) → C
5. OrthogonalLine(C, b) → d
6. Intersect(c, d) → D
7. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
8. Segment(C, B) → e
9. Segment(D, A) → f
10. Intersect(e, f) → E
11. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
12. Segment(I, G) → j
13. Segment(H, F) → k
14. Intersect(j, k) → J
15. Segment(K, L) → l
16. Circle(K, L) → p
17. Point(p) → M
18. Segment(K, M) → m
19. Line(M, l) → n
20. Line(L, m) → q
21. Intersect(n, q) → N
22. Segment(M, L) → r
23. Segment(N, K) → s
24. Intersect(r, s) → O
25. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
26. Rotate(C, (-α), E) → C'
27. Rotate(D, (-α), E) → D'
28. Rotate(B, (-α), E) → B'
29. Rotate(A, (-α), E) → A'
30. Polygon(C', D', B', A') → poly1', c', d', b', a'
31. Rotate(M, (-α), O) → M'
32. Rotate(N, (-α), O) → N'
33. Rotate(L, (-α), O) → L'
34. Rotate(K, (-α), O) → K'
35. Polygon(M', N', L', K') → poly3', m', n', l', k'
36. Segment(P, Q) → t
37. Segment(P, R) → e_1
38. Line(Q, e_1) → g_1
39. Line(R, t) → h_1
40. Intersect(g_1, h_1) → S
41. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
42. Segment(R, Q) → i_1
43. Segment(S, P) → j_1
44. Intersect(i_1, j_1) → T
45. Rotate(P, (-α), T) → P'
46. Rotate(R, (-α), T) → R'
47. Rotate(S, (-α), T) → S'
48. Rotate(Q, (-α), T) → Q'
49. Polygon(P', R', S', Q') → poly4', p', r', s', q'
50. Segment(U, V) → t_1
51. Segment(U, W) → a_2
52. Line(W, t_1) → b_2
53. Point(b_2) → Z
54. Segment(Z, V) → c_2
55. Polygon(U, V, Z, W) → poly5, u, v, z, w
56. Segment(W, V) → d_2
57. Segment(Z, U) → e_2
58. Intersect(d_2, e_2) → A_1
59. Rotate(U, (-α), A_1) → U'
60. Rotate(V, (-α), A_1) → V'
61. Rotate(Z, (-α), A_1) → Z'
62. Rotate(W, (-α), A_1) → W'
63. Polygon(U', V', Z', W') → poly5', u', v', z', w'
64. Line(B_1, C_1) → f_2
65. Mirror(D_1, f_2) → E_1
66. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
67. Segment(D_1, E_1) → g_2
68. Intersect(f_2, g_2) → F_1
69. Rotate(D_1, (-α), F_1) → G_1
70. Rotate(B_1, (-α), F_1) → H_1
71. Rotate(E_1, (-α), F_1) → I_1
72. Rotate(C_1, (-α), F_1) → J_1
73. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
74. Rotate(poly2, (-α), J) → poly2'
75. Rotate(C', (-(45°)), E) → C''
76. Rotate(D', (-(45°)), E) → D''
77. Rotate(B', (-(45°)), E) → B''
78. Rotate(A', (-(45°)), E) → A''