梯形面积计算与交互式探索

GeoGebra 命令及参数

1. Line(A, B) → f
2. Ray(A, B) → g
3. Point(g) → C
4. Ray(A, C) → h
5. Segment(A, C) → i
6. Slope(i) → m
7. PointIn(a) → D
8. Line(D, i) → j
9. Point(j) → E
10. Ray(D, E) → k
11. Point(k) → F
12. Segment(D, F) → l
13. Segment(A, D) → n
14. Segment(F, C) → p
15. Midpoint(p) → G
16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], C) → A'
17. Segment(A, A') → q
18. Dilate(C, If[1 < c ≤ 2, 2 - c, 0], G) → C'
19. Segment(C, C') → r
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. Segment(C'_1, C'') → r'
25. Dilate(F, If[4 < c ≤ 5, 5 - c, 0], D) → F'
26. Segment(F, F') → t
27. Dilate(D, If[5 < c ≤ 6, 6 - c, 0], A) → D'_6
28. Segment(D, D'_6) → d
29. Dilate(D, If[6.5 < c ≤ 7.5, 7.5 - c, 0], G) → D'_1
30. Polygon(A, C, G, D) → poly1, a_1, c_1, g_1, d_1
31. Polygon(G, F, D) → poly2, d_2, g_2, f_1
32. Segment(D, D'_1) → e
33. Rotate(G, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → G'_1
34. Rotate(F, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → F'_1
35. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_2
36. Polygon(G'_1, F'_1, D'_2) → poly2', d'_2, g'_1, f'_1
37. Segment(F'_1, D'_2) → h_1
38. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_3
39. Rotate(D'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → H
40. Segment(D'_3, H) → e'
41. Rotate(C'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → I
42. Rotate(C'', If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → C'''
43. Segment(I, C''') → r''
44. OrthogonalLine(D, q) → i_1
45. Intersect(f, q) → J
46. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], J) → D'_4
47. Segment(D, D'_4) → j_1
48. Min(t, q) → o
49. Circle(J, (0.15 * o)) → e_1
50. Intersect(e_1, i_1) → K, L
51. Intersect(e_1, f) → M, N
52. Angle(D, J, A) → α
53. Angle(C, A, D) → β
54. Intersect(i_1, f) → O
55. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], O) → D'_5
56. Segment(D, D'_5) → k_1
57. Angle(A, O, D) → γ
58. Point(f) → P
59. Point(f) → Q
60. Circle(C, t) → p_1
61. Intersect(p_1, f, 2) → R
62. Ray(R, Q) → m_1
63. Angle(F, C, A) → δ
64. Intersect(h_1, e') → D'_7
65. Intersect(h_1, e') → D'