梯形面积公式交互式探索

GeoGebra 命令及参数

1. Ray(A, B) → g
2. Point(g) → C
3. Segment(A, C) → i
4. Slope(i) → m
5. PointIn(a) → D
6. Midpoint(D, A) → S
7. Line(A, B) → f
8. Ray(A, C) → h
9. Line(D, i) → j
10. Point(j) → E
11. Ray(D, E) → k
12. Point(k) → F
13. Segment(D, F) → l
14. Segment(A, D) → n
15. Segment(F, C) → p
16. Midpoint(p) → G
17. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], C) → A'
18. Segment(A, A') → q
19. Dilate(C, If[1 < c ≤ 2, 2 - c, 0], G) → C'
20. Dilate(G, If[2 < c ≤ 3, 3 - c, 0], F) → G'
21. Segment(G, G') → s
22. Rotate(C, If[3 < c ≤ 4, ((c - 3) * π), π], G) → C'_1
23. Rotate(C', If[3 < c ≤ 4, ((c - 3) * π), π], G) → C''
24. Dilate(F, If[4 < c ≤ 5, 5 - c, 0], D) → F'
25. Segment(F, F') → t
26. Dilate(D, If[5 < c ≤ 6, 6 - c, 0], S) → D'
27. Dilate(D, If[6.5 < c ≤ 7.5, 7.5 - c, 0], G) → D'_1
28. Polygon(A, C, G, S) → poly1, e, f_1, g_1, k_1
29. Rotate(G, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → G'_1
30. Rotate(F, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → F'_1
31. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_2
32. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_3
33. Rotate(D'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → H
34. Rotate(C'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → I
35. Rotate(C'', If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → C'''
36. OrthogonalLine(D, q) → i_1
37. Intersect(f, q) → J
38. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], J) → D'_4
39. Segment(D, D'_4) → j_1
40. Min(t, q) → o
41. Circle(J, (0.15 * o)) → e_1
42. Intersect(e_1, i_1) → K, L
43. Intersect(e_1, f) → M, N
44. Angle(D, J, A) → α
45. Angle(C, A, D) → β
46. Intersect(i_1, f) → O
47. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], O) → D'_5
48. Point(f) → P
49. Point(f) → Q
50. Circle(C, t) → p_1
51. Intersect(p_1, f, 2) → R
52. Ray(R, Q) → m_1
53. Angle(F, C, A) → δ
54. Line(A, D) → l_1
55. Rotate(D, If[6 < c ≤ 7, ((-(c - 6)) * π), (-π)], S) → D'_6
56. Rotate(D', If[6 < c ≤ 7, ((-(c - 6)) * π), (-π)], S) → D''
57. Segment(F, C) → r
58. Segment(D, A) → d
59. Midpoint(D, O) → T
60. Polygon(S, G, F, D) → q1, s_1, g_2, f_2, d_1
61. Circle(A, (0.4 * Distance[A, S])) → c_1
62. Intersect(c_1, d, 1) → U
63. Intersect(c_1, q, 1) → V
64. Dilate(D, If[5 < c ≤ 6, 6 - c, 0], T) → D'_7
65. Segment(D, D'_7) → n_1
66. Dilate(T, If[6 < c ≤ 7, 7 - c, 0], O) → T'
67. Segment(T, T') → q_1
68. Angle(C, O, D) → γ
69. Rotate(D, If[7 < c ≤ 8 - ((c - 7) * π), (-π)], T) → D'_8
70. Rotate(D'_7, If[7 < c ≤ 8 - ((c - 7) * π), (-π)], T) → W
71. Rotate(D, If[7 < c ≤ 8, ((-(c - 7)) * π), (-π)], T) → D'_9
72. Rotate(D'_7, If[7 < c ≤ 8, ((-(c - 7)) * π), (-π)], T) → Z
73. Segment(D'_9, Z) → r_1
74. Dilate(T, If[8 < c ≤ 9, 9 - c, 0], S) → T'_1
75. Dilate(T, If[8 < c ≤ 9, 9 - c, 0], G) → T'_2
76. Segment(T, T'_2) → t_1
77. Segment(T, T'_1) → a_1
78. Angle(V, A, U) → ε
79. Rotate(V, If[9 < c ≤ 10, ((c - 9) * ε), ε], A) → V'
80. CircleSector(A, V, V') → h_1
81. Dilate(A, If[10.5 < c ≤ 11.5, 11.5 - c, 0], S) → A'_1
82. Vector(A, A'_1) → u
83. Translate(h_1, u) → c_2
84. Rotate(S, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → S'
85. Rotate(G, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → G'_2
86. Rotate(F, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → F'_2
87. Rotate(D, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → D'_{10}
88. Polygon(S', G'_2, F'_2, D'_{10}) → q1', s', g'_2, f'_2, d'_{10}
89. Rotate(F, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → F'_3
90. Rotate(F', If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → F''
91. Segment(F'_3, F'') → t'
92. Segment(G, F'_2) → b_1
93. Rotate(S, If[12 < c ≤ 13, ((-(c - 12)) * π), π], G) → S'_1
94. Segment(S'_1, D'_{10}) → h_2
95. Segment(S'_1, G) → i_2
96. Segment(F, G) → j_2
97. Segment(G, C) → k_2
98. Dilate(A, If[13 < c ≤ 14, 14 - c, 0], D'_{10}) → A'_2
99. Vector(A, A'_2) → v
100. Translate(h_1, v) → d_2