Geo-2017-Construction11-SimilarRightTriangles：相似直角三角形作图与性质探索

GeoGebra 命令及参数

1. Segment(A, B) → a
2. Midpoint(a) → C_1
3. OrthogonalLine(C_1, a) → b
4. Circle(C_1, A) → c
5. Semicircle(A, B) → d
6. Point(d) → C
7. Segment(A, C) → e
8. Segment(C, B) → f
9. OrthogonalLine(C, a) → g
10. Intersect(g, a) → E
11. Segment(C, E) → h
12. Angle(B, E, C) → α
13. Angle(A, C, B) → β
14. Polygon(A, E, C) → poly1, d_1, a_1, e_1
15. Polygon(E, B, C) → poly2, d_2, e_2, b_1
16. Circle(A, 1) → k
17. Circle(C, 1) → p
18. Circle(B, 1) → q
19. Intersect(p, e_1, 1) → F
20. Intersect(a_1, b_1) → G
21. Intersect(a_1, b_1) → H
22. Intersect(p, h, 1) → I
23. Intersect(p, f, 1) → J
24. Intersect(q, a, 1) → K
25. Intersect(q, f, 1) → L
26. Intersect(k, a, 1) → M
27. Intersect(k, e, 1) → N
28. CircleSector(A, M, N) → r
29. Dilate(C, If[-2 < i < -1, -1 - i, 0], E) → D'
30. Segment(C, D') → j
31. CircleSector(C, I, J) → s
32. CircleSector(B, L, K) → t
33. CircleSector(C, F, I) → c_1
34. Angle(C, E, A) → γ
35. Dilate(A, If[-0.5 < i < 0.5, 0.5 - i, 1], C) → A'
36. Vector(A, A') → u
37. Translate(r, u) → r'
38. Rotate(r', If[-0.5 < i < 0.5, (((-(i + 0.5)) * 90))°], A') → r''
39. CircleArc(A, M, N) → f_1
40. Dilate(B, If[0.5 < i < 1.5, 1.5 - i], C) → B'
41. Vector(B, B') → v
42. Translate(t, v) → t'
43. Rotate(t', If[0.5 < i < 1.5, (((i - 0.5) * 90))°], B') → t''
44. CircleArc(B, L, K) → g_1
45. Polygon(A, B, C) → poly3, d_3, a_2, b_2