直角三角形中的相似三角形：构造与对应边验证

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Segment(A, B) → g
4. Circle(B, 4) → c
5. Circle(A, 3) → d
6. Intersect(d, c) → C, D_{1}, ,
7. Segment(C, A) → f
8. Segment(C, B) → h
9. OrthogonalLine(C, g) → i
10. Intersect(i, g) → D
11. Segment(C, D) → j
12. Mirror(D, f) → D'
13. Point(eq1) → G
14. Point(Circle[G, 3]) → M
15. Segment(G, M) → m
16. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], D') → H
17. Segment(A, H) → k
18. Segment(H, C) → l
19. Segment(A, D) → n
20. Circle(G, n) → r
21. Circle(M, j) → s
22. Intersect(r, s) → E, I, ,
23. Dilate(D', If[1 < a ≤ 2, 2 - a, 0], E) → D''
24. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], G) → A'
25. Dilate(C, If[1 < a ≤ 2, 2 - a, 0], M) → C'
26. Segment(A', C') → q
27. Segment(C', D'') → t
28. Segment(D'', A') → b
29. Mirror(D, h) → N
30. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], N) → D'_{1}
31. Segment(C, D'_{1}) → e
32. Segment(D'_{1}, B) → f_1
33. Segment(D, B) → g_1
34. Point(Circle[F, h]) → J
35. Segment(F, J) → i_1
36. Circle(J, g_1) → c_1
37. Circle(F, j) → d_1
38. Intersect(d_1, c_1) → K, L, ,
39. Dilate(N, If[1 < a ≤ 2, 2 - a, 0], K) → N'
40. Dilate(C, If[1 < a ≤ 2, 2 - a, 0], F) → C'_{1}
41. Dilate(B, If[1 < a ≤ 2, 2 - a, 0], J) → B'
42. Segment(N', C'_{1}) → j_1
43. Segment(C'_{1}, B') → k_1
44. Segment(B', N') → l_1
45. Circle(A, 0.5) → e_1
46. Intersect(e_1, g, 1) → O
47. Intersect(e_1, f, 1) → P
48. CircleSector(A, O, P) → p_1
49. Dilate(A, If[0 < a ≤ 2, 2 - a, 0], G) → A'_{1}
50. Vector(A, A'_{1}) → u
51. Translate(p_1, u) → q_1
52. Dilate(B, If[0 ≤ a ≤ 2, 2 - a, 0], J) → B'_{1}
53. Circle(B, 0.5) → r_1
54. Intersect(r_1, h, 1) → Q
55. Intersect(r_1, g, 1) → R
56. CircleSector(B, Q, R) → s_1
57. Vector(B, B'_{1}) → v
58. Translate(s_1, v) → t_1
59. Circle(D, 0.3) → c_2
60. Intersect(c_2, j) → S,
61. Intersect(c_2, g) → T, U
62. OrthogonalLine(T, g) → m_1
63. OrthogonalLine(S, j) → n_1
64. Intersect(m_1, n_1) → V
65. Circle(E, 0.3) → d_2
66. Segment(E, M) → a_1
67. Segment(E, G) → b_1
68. Intersect(d_2, a_1) → W,
69. Intersect(d_2, b_1) → Z,
70. OrthogonalLine(Z, b_1) → f_2
71. OrthogonalLine(W, a_1) → g_2
72. Intersect(f_2, g_2) → A_1
73. Dilate(D, If[0 < a ≤ 2, 2 - a, 0], E) → D'_{2}
74. Dilate(S, If[0 < a ≤ 2, 2 - a, 0], W) → S'
75. Dilate(T, If[0 < a ≤ 2, 2 - a, 0], Z) → T'
76. Dilate(V, If[0 < a ≤ 2, 2 - a, 0], A_1) → V'
77. Polygon(T', D'_{2}, S', V') → q1, t', d'_{2}, s', v'
78. Polygon(D, S, V, T) → q2, d_3, s_2, v_1, t_2
79. Circle(K, 0.3) → e_2
80. Segment(K, J) → h_2
81. Segment(K, F) → i_2
82. Intersect(e_2, h_2) → B_1,
83. Intersect(e_2, i_2) → C_1,
84. OrthogonalLine(B_1, h_2) → j_2
85. OrthogonalLine(C_1, i_2) → k_2
86. Intersect(j_2, k_2) → E_1
87. Dilate(D, If[0 < a ≤ 2, 2 - a, 0], K) → D'_{3}
88. Dilate(S, If[0 < a ≤ 2, 2 - a, 0], C_1) → S'_{1}
89. Point(Circle[S, 0.3]) → F_1
90. Segment(S, F_1) → l_2
91. Point(Circle[D, 0.3]) → G_1
92. Segment(D, G_1) → m_2
93. Dilate(G_1, If[0 < a ≤ 2, 2 - a, 0], B_1) → H_1
94. Dilate(F_1, If[0 < a ≤ 2, 2 - a, 0], E_1) → I_1
95. Polygon(S'_{1}, I_1, H_1, D'_{3}) → q3, s'_{1}, n_2, p_2, d'_{3}
96. Polygon(D, G_1, F_1, S) → q4, d_4, q_2, r_2, s_3
97. Circle(C, 0.3) → c_3
98. Intersect(c_3, h) → J_1,
99. Intersect(c_3, f) → K_1,
100. OrthogonalLine(J_1, h) → a_2
101. OrthogonalLine(K_1, f) → b_2
102. Intersect(b_2, a_2) → L_1
103. Polygon(C, K_1, L_1, J_1) → q5, c_4, f_3, g_3, h_3