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角平分线构造演示

角平分线构造演示
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2017-02-17 17:52
圆角几何作图
本示例通过圆规和直尺动态演示角平分线的构造过程。核心概念包括角的平分线、圆、交点等。使用了Ray、Rotate、Angle、Circle、Intersect等GeoGebra命令。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Circle(A, b) → c
  6. Rotate(B, (a / 2 * π / 180), A) → B'_1
  7. Angle(B, A, B'_1) → β
  8. Ray(A, B'_1) → h
  9. Intersect(c, f, 1) → C
  10. Intersect(c, g) → D,
  11. OrthogonalLine(C, h) → i
  12. Intersect(i, h) → E
  13. Distance(C, E) → d
  14. Circle(C, e) → k
  15. Circle(D, e) → p
  16. Intersect(k, p, 2) → F
  17. Rotate(C, If[1 < j ≤ 2, (((j - 1) * 2) * π), (2 * π)], A) → C'
  18. CircleArc(A, C, C') → q
  19. Intersect(k, f, 1) → G
  20. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  21. Segment(A, A') → l
  22. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], G) → C'_1
  23. Segment(C, C'_1) → m
  24. Rotate(G, If[3 < j ≤ 4, (((j - 3) * 2) * π), (2 * π)], C) → G'
  25. CircleArc(C, G, G') → r
  26. Dilate(C, If[4 < j ≤ 5, 5 - j, 0], D) → C'_2
  27. Vector(C, C'_2) → u
  28. Translate(C, u) → C'_3
  29. Translate(C'_1, u) → H
  30. Segment(C'_3, H) → m'
  31. Rotate(H, If[5 < j ≤ 6, (((j - 5) * 2) * π), (2 * π)], D) → H'
  32. CircleArc(D, H, H') → s
  33. Angle(H, D, F) → γ
  34. Angle(H, D, H') → δ
  35. Circle(F, 2) → t
  36. Intersect(t, h, 2) → I
  37. Circle(A, (0.3 * b)) → c_1
  38. Intersect(c_1, h, 1) → J
  39. Intersect(f, l) → K
  40. Intersect(c_1, f) → L,
  41. CircleSector(A, L, J) → d_1
  42. Ray(F, I) → n
  43. Dilate(A, If[6 < j ≤ 7, 7 - j, 0], F) → A'_1
  44. Segment(A, A'_1) → f_1
  45. Rotate(L, If[7 < j ≤ 8, (((j - 7) * a / 2) * π / 180), (a / 2 * π / 180)], A) → L'
  46. CircleSector(A, L, L') → e_1
  47. Rotate(e_1, If[9 < j ≤ 10, (((j - 9) * a / 2) * π / 180), (a / 2 * π / 180)], A) → g_1