30°-60°-90°直角三角形交互探索

GeoGebra 命令及参数

1. Ray(B, C) → f
2. OrthogonalLine(C, f) → g
3. Rotate(C, π / 3, B) → B'
4. Angle(C, B, B') → α
5. Ray(B, B') → h
6. Intersect(g, h) → A
7. Segment(B, C) → i
8. Segment(C, A) → j
9. Segment(B, A) → k
10. Polygon(B, C, A) → poly1, c_1, a, b
11. Circle(A, (0.2 * i)) → e
12. Intersect(e, k) → D,
13. Intersect(e, j) → E,
14. CircleSector(A, D, E) → d
15. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → C'
16. Vector(A, C') → u
17. Translate(d, u) → d'
18. Rotate(d', If[1 < l ≤ 2, (((l - 1) * 2) * π / 3), (2 * π / 3)], B) → d''
19. Dilate(A, If[2 < l ≤ 3, 3 - l, 0], B) → C'_1
20. Vector(A, C'_1) → v
21. Translate(d, v) → d'_1
22. Rotate(d'_1, If[3 < l ≤ 4, (((-(l - 3)) * 7) * π / 6), (-7 * π / 6)], B) → p
23. Dilate(A, If[4 < l ≤ 5, 5 - l, 0], C) → C'_2
24. Vector(A, C'_2) → w
25. Translate(d, w) → d'_2
26. Dilate(A, If[6 < l ≤ 7, 7 - l, 0], C) → C'_3
27. Vector(A, C'_3) → m
28. Translate(d, m) → d'_3
29. Rotate(d'_2, If[5 < l ≤ 6, ((-(l - 5)) * π / 2), ((-π)) / 2], C) → q
30. Rotate(d'_3, If[7 < l ≤ 8, (((l - 7) * 4) * π / 3), (4 * π / 3)], C) → r
31. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], C) → C'_4
32. Vector(A, C'_4) → n
33. Translate(d, n) → d'_4
34. Rotate(d'_4, If[9 < l ≤ 10, (((l - 9) * 7) * π / 6), (7 * π / 6)], C) → s
35. Midpoint(B, A) → F
36. Dilate(B, If[10 < l ≤ 11, 11 - l, 0], C) → A'
37. Segment(B, A') → t
38. Rotate(B, If[11 < l ≤ 12, ((l - 11) * π / 3), π / 3], B) → A'_1
39. Rotate(A', If[11 < l ≤ 12, ((l - 11) * π / 3), π / 3], B) → A''
40. Segment(A'_1, A'') → t'
41. Dilate(B, If[12 < l ≤ 13, 13 - l, 0], F) → A'_2
42. Vector(B, A'_2) → u_1
43. Translate(B, u_1) → A'_3
44. Translate(A', u_1) → A''_1
45. Segment(A'_3, A''_1) → t'_1
46. Rotate(A'_3, If[13 < l ≤ 14, ((l - 13) * π / 3), π / 3], F) → G
47. Rotate(A''_1, If[13 < l ≤ 14, ((l - 13) * π / 3), π / 3], F) → H
48. Segment(G, H) → f_1
49. Angle(B, A, C) → β
50. Angle(C, B, A) → γ
51. Angle(A, C, B) → δ