通过拖动点验证勾股定理的动态几何证明

GeoGebra 命令及参数

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Midpoint(A, B) → F
4. Segment(F, B) → b
5. Point(b) → C
6. Semicircle(A, B) → c
7. Semicircle(A, C) → d
8. Point(d) → D
9. CircumcircleSector(A, D, C) → e
10. Point(c) → E
11. CircumcircleSector(A, E, B) → f
12. Point(xAxis) → G
13. CircleSector(G, H, I) → h
14. Semicircle(I, H) → k
15. Segment(A, F) → i
16. Segment(I, H) → j
17. Circle(F, B) → p
18. Circle(A, C) → q
19. Intersect(p, q, 1) → J
20. Midpoint(A, J) → K
21. CircleSector(K, A, J) → r
22. Midpoint(B, J) → L
23. CircleSector(L, J, B) → s
24. Midpoint(A, C) → M
25. If(0 ≤ l ≤ 1, 1 - l, If[1 < l, 0, 1]) → d1
26. Dilate(M, d1, K) → M'
27. Vector(M, M') → u
28. Translate(A, u) → A'
29. Translate(D, u) → D'
30. Translate(C, u) → C'
31. CircumcircleSector(A', D', C') → e'
32. Angle(B, A, J) → α
33. If(0 ≤ l ≤ 1, l, If[1 < l, 1, 0]) → r1
34. Rotate(A', ((180° - α) * r1), M') → A''
35. Rotate(D', ((180° - α) * r1), M') → D''
36. Rotate(C', ((180° - α) * r1), M') → C''
37. CircumcircleSector(A'', D'', C'') → e''
38. If(1 ≤ l ≤ 2, 2 - l, If[2 < l, 0, 1]) → d2
39. Dilate(G, d2, L) → G'
40. Vector(G, G') → v
41. Translate(h, v) → h'
42. Angle(A, B, J) → β
43. If(1 ≤ l ≤ 2, l - 1, If[2 < l, 1, 0]) → r2
44. Rotate(h', (-(((180° - β) * r2))), G') → h''
45. Segment(A, B) → m