梯形面积的推导

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Line(C, f) → g
3. Segment(A, C) → h_1
4. Point(g) → D
5. Segment(B, D) → i
6. Polygon(A, C, D, B) → poly1, c, a, d, b
7. Point(f) → E
8. OrthogonalLine(E, a) → h_2
9. Intersect(h_2, a) → F
10. Segment(E, F) → h
11. Vector(I, J) → v
12. Vector(G, H) → u
13. Translate(A, u) → A'
14. Translate(C, u) → C'
15. Translate(D, u) → D'
16. Translate(B, u) → B'
17. Polygon(A', C', D', B') → poly1', a', c', d', b'
18. Translate(A', v) → A''
19. Translate(C', v) → C''
20. Translate(D', v) → D''
21. Translate(B', v) → B''
22. Polygon(A'', C'', D'', B'') → poly1'', a'', c'', d'', b''
23. Translate(A, v) → A'_1
24. Translate(C, v) → C'_1
25. Translate(D, v) → D'_1
26. Translate(B, v) → B'_1
27. Polygon(A', C', B') → poly2, b'_2, a'_2, c'_2
28. Polygon(C', D', B') → poly3, b'_3, c'_3, d'_2
29. Rotate(B', (-Rotate), B') → B''_1
30. Midpoint(D', B') → K
31. Rotate(C', (-Rotate), K) → C''_1
32. Rotate(D', (-Rotate), K) → D''_1
33. Rotate(B', (-Rotate), K) → B''_2
34. Polygon(C''_1, D''_1, B''_2) → poly3', b''_2, c''_1, d''_1
35. Midpoint(A'', C'') → L
36. Midpoint(B'', D'') → M
37. Polygon(A'', L, M, B'') → poly4, a''_1, l, m, b''_1
38. Polygon(L, C'', D'', M) → poly5, l_1, c''_2, d''_2, m_1
39. Rotate(L, (-Rotate), M) → L'
40. Rotate(C'', (-Rotate), M) → C'''
41. Rotate(D'', (-Rotate), M) → D'''
42. Rotate(M, (-Rotate), M) → M'
43. Polygon(L', C''', D''', M') → poly5', l', c''', d''', m'
44. Midpoint(A'_1, C'_1) → N
45. Midpoint(D'_1, B'_1) → O
46. Rotate(N, (-Rotate), N) → N'
47. Rotate(A'_1, (-Rotate), N) → R
48. Rotate(O, Rotate, O) → O'
49. Rotate(B'_1, Rotate, O) → S
50. Angle(F, E, A) → α
51. Translate(A'', v) → A'''
52. Translate(C'', v) → C'''_1
53. Translate(D'', v) → D'''_1
54. Translate(B'', v) → B'''
55. Polygon(A''', C'''_1, D'''_1, B''') → poly1''', a''', c'''_1, d'''_1, b'''
56. Midpoint(a''') → T
57. Midpoint(d'''_1) → U
58. OrthogonalLine(C'''_1, b''') → t
59. OrthogonalLine(D'''_1, b''') → e
60. OrthogonalLine(A''', c'''_1) → f_1
61. OrthogonalLine(B''', c'''_1) → g_1
62. OrthogonalLine(T, b''') → i_1
63. OrthogonalLine(U, b''') → j_1
64. Intersect(i_1, b''') → V
65. Intersect(j_1, b''') → W
66. Polygon(V, T, C'''_1, D'''_1, U, W) → poly9, v_1, t_1, c'''_2, d'''_2, u_1, w
67. Polygon(A''', T, V) → poly10, v_2, a'''_1, t_2
68. Polygon(W, U, B''') → poly11, b'''_1, w_1, u_2
69. Rotate(A''', (-Rotate), T) → Z
70. Rotate(T, (-Rotate), T) → T'
71. Rotate(V, (-Rotate), T) → V'
72. Polygon(Z, T', V') → poly10', v', z_1, t'
73. Rotate(W, Rotate, U) → W'
74. Rotate(U, Rotate, U) → U'
75. Rotate(B''', Rotate, U) → A_1
76. Polygon(W', U', A_1) → poly11', a_1, w', u'
77. Intersect(i_1, c'''_1) → B_1
78. Polygon(B_1, D'''_1, U, W, A''', T) → poly12, b_1, d'''_3, u_3, w_2, a'''_2, t_3
79. Polygon(C'''_1, B_1, T) → poly13, t_4, c'''_3, b_2
80. Rotate(C'''_1, Rotate, T) → C_1
81. Rotate(B_1, Rotate, T) → D_1
82. Rotate(T, Rotate, T) → T'_1
83. Polygon(C_1, D_1, T'_1) → poly13', t'_1, c_1, d_1
84. Intersect(j_1, c'''_1) → E_1
85. Polygon(B_1, T, A''', B''', U, E_1) → poly14, b_3, t_5, a'''_3, b'''_2, u_4, e_1
86. Polygon(U, E_1, D'''_1) → poly15, d'''_4, u_5, e_2
87. Rotate(U, (-Rotate), U) → U'_1
88. Rotate(E_1, (-Rotate), U) → F_1
89. Rotate(D'''_1, (-Rotate), U) → G_1
90. Polygon(U'_1, F_1, G_1) → poly15', g_2, u'_1, f_2
91. Polygon(V, T, C'''_1, E_1, U, B''') → poly16, v_3, t_6, c'''_4, e_3, u_6, b'''_3
92. PointIn(poly1) → Pointpoly1