等腰梯形对角线的证明

GeoGebra 命令及参数

1. Line(A, B) → a
2. Ray(A, B) → b
3. Point(b) → C
4. Midpoint(A, C) → D
5. Line(A, C) → c
6. Slope(c) → d
7. OrthogonalLine(D, c) → g
8. Point(g) → E
9. Ray(D, E) → h
10. Point(h) → F
11. Slope(h) → i
12. Line(F, c) → l
13. Point(l) → G
14. Point(l) → H
15. Ray(F, G) → m
16. Ray(F, H) → n
17. Point(m) → I
18. Mirror(I, h) → I'
19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
20. Segment(A, A') → p
21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], I) → A'_1
22. Segment(A, A'_1) → q
23. Segment(A, C) → r
24. Segment(C, I') → s
25. Segment(I', I) → t
26. Segment(I, A) → a_1
27. Circle(A, (0.2 * Min[a_1, r])) → c_1
28. Circle(I, (0.2 * Min[a_1, r])) → d_1
29. Intersect(d_1, a_1, 1) → J
30. Intersect(d_1, t, 1) → K
31. Intersect(c_1, r, 1) → L
32. Intersect(c_1, a_1, 1) → M
33. Dilate(I, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
34. Segment(I, I'_1) → b_1
35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_2
36. Vector(A, A'_2) → u
37. Translate(A, u) → A'_3
38. Translate(A'_1, u) → N
39. Segment(A'_3, N) → q'
40. OrthogonalLine(A, r) → g_1
41. Point(g_1) → O
42. Angle(I, A, O) → α
43. Angle(I', C, A) → β
44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → P
45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → N'
46. Segment(P, N') → q''
47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_4
48. Vector(A, A'_4) → v
49. Dilate(I, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
50. Vector(I, I'_2) → w
51. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], I') → A'_5
52. Segment(A, A'_5) → i_1
53. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], I) → A'_6
54. Vector(A, A'_6) → u_1
55. Translate(A, u_1) → A'_7
56. Translate(A'_5, u_1) → Q
57. Segment(A'_7, Q) → j_1
58. Segment(I, C) → l_1
59. Angle(L, A, I') → γ
60. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], I) → R
61. Rotate(Q, If[7 < o ≤ 8, (((-(o - 7)) * 2) * γ), (-2 * γ)], I) → Q'
62. Segment(R, Q') → m_1
63. Polygon(A, C, I', I) → poly1, a_2, c_2, i', i_2