勾股定理的几何证明

GeoGebra 命令及参数

1. Point(Segment[A, B]) → E
2. Polygon(A, B, 4) → square1, f, g, h, i, C, D
3. Translate(E, Vector[((2 * f) + spacer - Segment[B, E], 0)]) → E'
4. Translate(D, Vector[E' - D]) → D'
5. Translate(square1, (f + spacer, 0)) → square2
6. Polygon(A, F, E) → t1, e, a, f_1
7. Polygon(F, D, G) → t2, g_1, f_2, d
8. Polygon(G, H, C) → t3, c, g_2, h_1
9. Polygon(E, B, H) → t4, h_2, e_1, b
10. Translate(A, Vector[((2 * f) + spacer - Segment[B, E], 0)]) → A'
11. Translate(F, Vector[((2 * f) + spacer - Segment[B, E], 0)]) → F'
12. Polygon(A', F', E') → t1', e', a', f'
13. Translate(G, Vector[F' - G]) → G'
14. Translate(H, Vector[F' - G]) → H'
15. Translate(C, Vector[F' - G]) → C'
16. Polygon(G', H', C') → t3', c', g', h'
17. Translate(E, (f + spacer, 0)) → E'_1
18. Translate(B, (f + spacer, 0)) → B'
19. Translate(H, (f + spacer, 0)) → H'_1
20. Polygon(E'_1, B', H'_1) → t4', h'_1, e'_1, b'
21. Translate(G, Vector[E' - D]) → G'_1
22. Translate(F, Vector[D' - D]) → F'_1
23. Polygon(F'_1, D', G'_1) → t2', g'_1, f'_1, d'
24. Translate(A, Vector[(n * Vector[((2 * f) + spacer - Segment[B, E], 0)])]) → A'_1
25. Translate(F, Vector[(n * Vector[((2 * f) + spacer - Segment[B, E], 0)])]) → F'_2
26. Translate(E, Vector[(n * Vector[((2 * f) + spacer - Segment[B, E], 0)])]) → E'_2
27. Polygon(A'_1, F'_2, E'_2) → t1'', e'_2, a'_1, f'_2
28. Translate(F, Vector[(n * Vector[G, G'_1])]) → F'_3
29. Translate(D, Vector[(n * Vector[G, G'_1])]) → D'_1
30. Translate(G, Vector[(n * Vector[G, G'_1])]) → G'_2
31. Polygon(F'_3, D'_1, G'_2) → t2'', g'_2, f'_3, d'_1
32. Translate(G, Vector[(n * Vector[G, F'])]) → G'_3
33. Translate(H, Vector[(n * Vector[G, F'])]) → H'_2
34. Translate(C, Vector[(n * Vector[G, F'])]) → C'_1
35. Polygon(G'_3, H'_2, C'_1) → t3'', c'_1, g'_3, h'_2
36. Translate(E, Vector[(n * Vector[B, B'])]) → E'_3
37. Translate(B, Vector[(n * Vector[B, B'])]) → B'_1
38. Translate(H, Vector[(n * Vector[B, B'])]) → H'_3
39. Polygon(E'_3, B'_1, H'_3) → t4'', h'_3, e'_3, b'_1
40. Polygon(E', A', 4) → aSquared, j, k, l, m, I, J
41. Polygon(D', G'_1, 4) → bSquared, p, q, r, s, K, L
42. Point(i) → M
43. Point(h) → N
44. Polygon(E, F, G, H) → q1, t, i_1, j_1, k_1
45. Angle(B, A, D) → α
46. Angle(B', I, G') → β
47. Angle(E, F, G) → γ
48. LaTeX("\text{\textbf{Question: }How do the parts of Square 1 relate to the parts of Square 2?}") → instruction1
49. LaTeX("\text{\textbf{Instructions: }Move the slider to visualize the relationship between Square 1\\and Square 2. Drag point \(B\) in Square 1 to change the size of the triangles.}") → instruction2