直角三角形中的高线——有何特殊之处？

GeoGebra 命令及参数

1. Segment(A, B) → f
2. OrthogonalLine(A, f) → g
3. Point(g) → C
4. Segment(B, C) → h
5. Angle(f, g) → α
6. Segment(C, A) → i
7. OrthogonalLine(A, h) → j
8. Angle(h, j) → β
9. Intersect(j, h) → D
10. Segment(D, A) → k
11. Polygon(C, A, D) → poly1, d, c, a
12. Polygon(A, B, D) → poly2, d_1, a_1, b
13. Mirror(C, i) → C'
14. Mirror(A, i) → A'
15. Mirror(D, i) → D'
16. Polygon(C', A', D') → poly5, d', c', a'
17. Mirror(A, f) → A'_1
18. Mirror(B, f) → B'
19. Mirror(D, f) → D'_1
20. Polygon(A'_1, B', D'_1) → poly2', d'_1, a'_1, b'
21. Polygon(C, A, B) → poly3, b_1, c_1, a_2
22. Point(g) → E
23. Angle(E, A, D'_1) → γ
24. Point(g) → F
25. Rotate(A'_1, If[0 < e ≤ 1, ((-e) * γ), (-γ)], A) → G
26. Rotate(B', If[0 < e ≤ 1, ((-e) * γ), (-γ)], A) → B''
27. Rotate(D'_1, If[0 < e ≤ 1, ((-e) * γ), (-γ)], A) → H
28. Polygon(G, B'', H) → poly4, h_1, g_1, b''
29. Vector(H, A) → u
30. Dilate(H, If[1.5 < e < 2.5, 2.5 - e, 0], A) → H'
31. Vector(H, H') → v
32. Translate(G, v) → G'
33. Translate(B'', v) → B'''
34. Translate(H, v) → H'_1
35. Polygon(G', B''', H'_1) → poly4', h'_1, g', b'''
36. Line(A, B) → l
37. Point(l) → I
38. Angle(D', A, I) → δ
39. Rotate(C', If[3 < e < 4, (δ * (e - 3)), δ], A) → C''
40. Rotate(A', If[3 < e < 4, (δ * (e - 3)), δ], A) → A''
41. Rotate(D', If[3 < e < 4, (δ * (e - 3)), δ], A) → D''
42. Polygon(C'', A'', D'') → poly5', d'', c'', a''
43. Dilate(D'', If[4 < e < 5, 5 - e, 0], A) → D'''
44. Vector(D'', D''') → w
45. Translate(C'', w) → C'''
46. Translate(A'', w) → A'''
47. Translate(D'', w) → D'''_1
48. Polygon(C''', A''', D'''_1) → poly5'', d'''_1, c''', a'''
49. Segment(C''', A''') → p
50. Segment(A''', D'''_1) → q
51. Segment(C''', D'''_1) → r
52. Point(f) → J
53. Point(i) → L
54. Circle(C''', L) → s_1
55. Circle(A''', J) → t
56. Intersect(s_1, p) → K,
57. Intersect(t, p) → M,
58. CircleSector(C''', L, K) → e_1
59. CircleSector(A''', M, J) → f_1
60. Intersect(f_1, f, 1) → N
61. Dilate(C''', If[0 ≤ s ≤ 1, 1 - s, 0], G') → O
62. Dilate(A''', If[0 ≤ s ≤ 1, 1 - s, 0], B''') → P
63. Vector(C''', O) → u_1
64. Vector(A''', P) → v_1
65. Translate(e_1, u_1) → k_1
66. Translate(f_1, v_1) → p_1
67. Dilate(C''', If[1 ≤ s ≤ 2, 2 - s, 0], C) → Q
68. Dilate(A''', If[1 ≤ s ≤ 2, 2 - s, 0], B) → R
69. Vector(C''', Q) → w_1
70. Vector(A''', R) → i_1
71. Translate(e_1, w_1) → q_1
72. Translate(f_1, i_1) → r_1