菱形角度探究：构造、旋转与角平分线

GeoGebra 命令及参数

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') → HH
24. Intersect(j, d') → II
25. Intersect(n, j) → R
26. Intersect(n, a_1) → S
27. Segment(R, S) → p
28. Segment(F, S) → q
29. Mirror(F, g) → H
30. Mirror(G, g) → I
31. Segment(I, E) → r
32. CircleArc(E, B, H) → t
33. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
34. Rotate(I, (((s - 3) * 180))°, r) → I'
35. Rotate(E, (((s - 3) * 180))°, r) → E'_1
36. Rotate(B, (((s - 3) * 180))°, r) → B'
37. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
38. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
39. Segment(B, E) → h_1
40. Segment(B, I) → j_1
41. Mirror(R, g) → TT
42. Mirror(S, g) → SS
43. Segment(SS, TT) → k_1
44. Segment(SS, H) → l_1
45. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
46. Circle(G, C) → p_1
47. Intersect(d', f_1) → J
48. Intersect(d', f_1) → K
49. Intersect(d', f_1) → L
50. Intersect(d', f_1) → M
51. Intersect(p_1, f_1) → N,
52. CircleArc(G, N, C) → q_1
53. Line(G, F) → m_1
54. Intersect(m_1, a_2) → O
55. Segment(O, F) → n_1
56. Polygon(O, C, G) → driehoek5, g_5, o, c_3
57. Rotate(O, (((s - 5) * 180))°, c_3) → O'
58. Rotate(C, (((s - 5) * 180))°, c_3) → C'
59. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
60. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
61. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
62. Mirror(O, n_1) → O'_1
63. Mirror(C, n_1) → C'_1
64. Mirror(G, n_1) → G'_2
65. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
66. Mirror(O, g) → O'_2
67. Mirror(C, g) → C'_2
68. Mirror(G, g) → G'_3
69. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
70. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
71. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
72. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
73. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
74. Intersect(c', o_1) → V
75. Intersect(c', o_1) → W
76. Intersect(c', o_1) → Z
77. Line(I, H) → r_1
78. Intersect(o_1, r_1) → T
79. Segment(O, C) → s_1
80. Segment(C, G) → t_1
81. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
82. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
83. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
84. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
85. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
86. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
87. Segment(E, T) → f_2
88. Segment(T, E) → j_2
89. Intersect(Segment[O, N], j_2) → A_1
90. Segment(A_1, E) → k_2
91. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
92. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
93. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
94. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
95. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
96. Mirror(N, g) → NN
97. CircleArc(I, A, NN) → d_2
98. Segment(I, T) → l_2
99. Intersect(g'_2, l_2) → B_1
100. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
101. Segment(I, A) → m_2
102. Segment(A, O) → p_2
103. Line(E, T) → q_2
104. Line(I, G) → r_2
105. Segment(I, E) → s_2
106. Segment(E, G) → f_3
107. Segment(I, T) → h_3
108. Segment(T, G) → j_3
109. Segment(I, G) → k_3
110. Segment(E, T) → l_3
111. Midpoint(E, T) → D_1
112. Angle(G, D_1, E) → α
113. Angle(I, D_1, T) → β
114. Angle(D, G, E) → γ
115. Angle(T, G, C) → δ
116. Angle(E, G, T) → ε
117. Angle(E, I, B) → ζ
118. Angle(T, I, E) → η
119. Angle(A, I, T) → θ
120. Angle(T, I, E) → ι
121. Angle(E, G, T) → κ
122. Angle(I, E, G) → λ
123. Angle(G, T, I) → μ