Exploring Angles in a Hexagon

GeoGebra Commands & Parameters

1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
2. Segment((sqrt(2) / 4, 0), (sqrt(2) / 4, 1)) → f
3. Segment((sqrt(2) / 2, 0), (sqrt(2) / 2, 1)) → g
4. Segment(((3 * sqrt(2) / 4), 0), ((3 * sqrt(2) / 4), 1)) → h
5. Midpoint(B, D) → E
6. Rotate(D, -90°, E) → DD
7. CircleArc(E, DD, D) → e
8. Intersect(e, h, 1) → F
9. CircleArc(E, F, D) → k
10. AngularBisector(F, E, D) → i
11. Intersect(i, c) → G
12. Segment(E, G) → j
13. Polygon(A, C, G, E, B) → veelhoek1, a_1, c_1, g_1, e_1, b_1
14. Polygon(E, D, G) → driehoek1, g_2, e_2, d_1
15. Rotate(E, (((-(s - 1)) * 180))°, g_1) → E'
16. Rotate(D, (((-(s - 1)) * 180))°, g_1) → D'
17. Rotate(G, (((-(s - 1)) * 180))°, g_1) → G'
18. Polygon(E', D', G') → driehoek1', g', e', d'
19. Polygon(E, F, G) → driehoek2, g_3, e_3, f_1
20. Segment(E, D) → l
21. Segment(D, G) → m
22. OrthogonalLine(F, a_1) → n
23. Intersect(j, d') → II
24. Intersect(n, j) → R
25. Intersect(n, a_1) → S
26. Segment(R, S) → p
27. Segment(F, S) → q
28. Mirror(F, g) → H
29. Mirror(G, g) → I
30. Segment(I, E) → r
31. CircleArc(E, B, H) → t
32. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
33. Rotate(I, (((s - 3) * 180))°, r) → I'
34. Rotate(E, (((s - 3) * 180))°, r) → E'_1
35. Rotate(B, (((s - 3) * 180))°, r) → B'
36. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
37. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
38. Segment(B, E) → h_1
39. Segment(B, I) → j_1
40. Mirror(R, g) → TT
41. Mirror(S, g) → SS
42. Segment(SS, TT) → k_1
43. Segment(SS, H) → l_1
44. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
45. Circle(G, C) → p_1
46. Intersect(d', f_1) → J
47. Intersect(d', f_1) → K
48. Intersect(d', f_1) → L
49. Intersect(d', f_1) → M
50. Intersect(p_1, f_1) → N,
51. CircleArc(G, N, C) → q_1
52. Line(G, F) → m_1
53. Intersect(m_1, a_2) → O
54. Segment(O, F) → n_1
55. Polygon(O, C, G) → driehoek5, g_5, o, c_3
56. Rotate(O, (((s - 5) * 180))°, c_3) → O'
57. Rotate(C, (((s - 5) * 180))°, c_3) → C'
58. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
59. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
60. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
61. Mirror(O, n_1) → O'_1
62. Mirror(C, n_1) → C'_1
63. Mirror(G, n_1) → G'_2
64. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
65. Mirror(O, g) → O'_2
66. Mirror(C, g) → C'_2
67. Mirror(G, g) → G'_3
68. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
69. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
70. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
71. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
72. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
73. Intersect(c', o_1) → V
74. Intersect(c', o_1) → W
75. Intersect(c', o_1) → Z
76. Line(I, H) → r_1
77. Intersect(o_1, r_1) → T
78. Segment(O, C) → s_1
79. Segment(C, G) → t_1
80. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
81. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
82. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
83. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
84. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
85. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
86. Segment(E, T) → f_2
87. Segment(T, E) → j_2
88. Intersect(Segment[O, N], j_2) → A_1
89. Segment(A_1, E) → k_2
90. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
91. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
92. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
93. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
94. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
95. Mirror(N, g) → NN
96. CircleArc(I, A, NN) → d_2
97. Segment(I, T) → l_2
98. Intersect(g'_2, l_2) → B_1
99. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
100. Segment(I, A) → m_2
101. Segment(A, O) → p_2
102. Mirror(H, Segment[I, G]) → HH
103. Mirror(HH, g) → GG
104. Intersect(n_2, g) → C_1
105. Polygon(I, T, C_1, NN) → vierhoek5, i_7, t_5, c_4, nn
106. Segment(HH, H) → q_2
107. Segment(GG, F) → r_2
108. Polygon(GG, F, G) → driehoek6, g_9, gg, f_3
109. Polygon(I, H, HH) → driehoek7, hh, i_8, h_3
110. Rotate(GG, (((s - 9) * 180))°, q) → GG'
111. Rotate(F, (((s - 9) * 180))°, q) → F'
112. Rotate(G, (((s - 9) * 180))°, q) → G'_5
113. Polygon(GG', F', G'_5) → driehoek6', g'_5, gg', f'
114. Rotate(I, (((s - 9) * 180))°, f) → I'_3
115. Rotate(H, (((s - 9) * 180))°, f) → H'
116. Rotate(HH, (((s - 9) * 180))°, f) → HH'
117. Polygon(I'_3, H', HH') → driehoek7', hh', i'_3, h'
118. Segment(HH, E) → s_2
119. Segment(H, B_1) → j_3
120. Segment(E, GG) → k_3
121. Segment(T, F) → l_3
122. Polygon(E, HH, H, T, F, GG) → veelhoek4, e_9, hh_1, h_4, t_6, f_4, gg_1
123. Segment(C_1, T) → m_3
124. Angle(HH, E, GG) → α
125. Angle(HH, E, GG) → β
126. Angle(H', HH, E) → γ
127. Angle(T, H', HH) → δ
128. Angle(F, T, H') → ε
129. Angle(GG, F, T) → ζ
130. Angle(E, GG, F) → η