梯形中位线：两种“无字证明”发现

GeoGebra 命令及参数

1. Ray(A, B) → a
2. Segment(A, B) → b
3. Line(C, b) → c
4. Point(c) → D
5. Ray(C, D) → d
6. Point(d) → E
7. Segment(C, A) → e
8. Segment(C, E) → f
9. Segment(E, B) → g
10. Polygon(A, B, E, C) → poly1, a_1, b_1, e_1, c_1
11. Midpoint(e) → F
12. Midpoint(g) → G
13. Segment(F, G) → h
14. Rotate(A, (-α), G) → A'
15. Rotate(B, (-α), G) → B'
16. Rotate(E, (-α), G) → E'
17. Rotate(C, (-α), G) → C'
18. Polygon(A', B', E', C') → poly1', a', b', e', c'
19. Rotate(F, (-α), G) → F'
20. Rotate(G, (-α), G) → G'
21. Segment(F', G') → h'
22. Segment(B', A') → i
23. Segment(A', C') → j
24. Segment(C', E') → k
25. Segment(E', B') → l
26. Segment(C, F) → m
27. Segment(F, A) → n
28. Segment(E, G) → p
29. Segment(G, B) → q
30. Segment(C', F') → r
31. Segment(F', A') → s
32. Line(C, A) → t
33. Circle(F, 1) → f_1
34. Intersect(f_1, h, 1) → J
35. Intersect(t, m) → K
36. Intersect(t, m) → L
37. Intersect(f_1, t) → M, N
38. CircleSector(F, J, M) → h_1
39. Dilate(F, 1 - o, A) → F'_1
40. Dilate(F, 1 - o, C) → F'_2
41. Vector(F, F'_2) → u
42. Vector(F, F'_1) → v
43. Translate(h_1, v) → k_1
44. Translate(h_1, u) → p_1
45. Dilate(F, If[0 < w ≤ 1, 1 - w, 0], C) → F'_3
46. Vector(F, F'_3) → u_1
47. Translate(G, u_1) → G'_1
48. Segment(F'_3, G'_1) → d_1
49. Dilate(F, If[1 < w ≤ 2, 2 - w, 0], C) → F'_4
50. Vector(F, F'_4) → v_1
51. Translate(F', v_1) → F''
52. Translate(G, v_1) → G'_2
53. Segment(G'_2, F'') → g_1