经典面积计算与勾股逆定理演示

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Segment(P, B) → j
3. Segment(P, C) → k
4. Segment(P, A) → l
5. OrthogonalLine(C, j) → m
6. OrthogonalLine(A, j) → p
7. OrthogonalLine(D, p) → q
8. Line(P, B) → r
9. Intersect(p, r) → E
10. Intersect(m, r) → F
11. Intersect(m, q) → G
12. Intersect(p, q) → H
13. Segment(B, F) → s
14. Segment(A, E) → t
15. Segment(D, H) → b
16. Segment(C, G) → c
17. Polygon(I, J, 4) → poly2, e, f_1, g_1, h_1, K, L
18. Segment(M, J) → i_1
19. Segment(M, I) → j_1
20. Segment(M, K) → k_1
21. Line(M, J) → l_1
22. OrthogonalLine(I, l_1) → m_1
23. OrthogonalLine(K, l_1) → n_1
24. OrthogonalLine(L, m_1) → p_1
25. Intersect(m_1, p_1) → N
26. Intersect(l_1, m_1) → O
27. Intersect(l_1, n_1) → Q
28. Intersect(n_1, p_1) → R
29. Segment(I, O) → q_1
30. Segment(J, Q) → r_1
31. Segment(K, R) → s_1
32. Segment(L, N) → t_1
33. Semicircle(A_3, B_3) → d
34. Point(d) → T
35. Segment(T, B_3) → a_1
36. Ray(A_3, T) → b_1
37. Point(a_1) → U
38. Circle(A_3, Distance[U, B_3]) → c_1
39. Intersect(c_1, b_1, 1) → D_3
40. Circle(D_3, 10) → d_1
41. Intersect(d_1, a_1, 1) → C_3
42. Segment(D_3, C_3) → e_1
43. Segment(C_3, B_3) → f_2
44. Segment(A_3, B_3) → g_2
45. Segment(A_3, D_3) → h_2
46. Angle(A_3, T, B_3) → α
47. Rotate(Translate[lpline3, Vector[A_3, B_3]], 90°, B_3) → lpline3_2
48. Rotate(Translate[lpline3_2, Vector[A_3, B_3]], 90°, B_3) → lpline3_3
49. Rotate(Translate[lpline3_3, Vector[A_3, B_3]], 90°, B_3) → lpline3_4
50. Segment(A_4, B_4) → i_2
51. Semicircle(A_4, B_4) → c_2
52. Semicircle(B_4, A_4) → d_2
53. Circle(A_4, 16) → e_2
54. Intersect(c_2, e_2, 1) → C_4
55. Segment(A_4, C_4) → j_2
56. Segment(C_4, B_4) → k_2
57. Semicircle(C_4, A_4) → p_2
58. Semicircle(B_4, C_4) → q_2
59. Midpoint(k_2) → O_1
60. Midpoint(j_2) → O_2
61. Intersect(p_2, i_2, 2) → D_4
62. Point(larea41) → M_4
63. Locus(M'_4, M_4) → loc1
64. Point(larea42) → M4
65. Locus(M4', M4) → loc2
66. Point(larea43) → M3
67. Locus(M3', M3) → loc3