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动态等边三角形构造演示

动态等边三角形构造演示
几何画板及绘图内容加载中，请稍等……
2019-10-16 21:00
测试改名0向量几何作图
①本范例动态演示了由任意三角形两边构建等边三角形的几何问题；②涉及核心概念：全等、等边三角形、向量、变换；③构造要点：使用Segment, Rotate, Angle, Point, Polygon, Midpoint, Vector, Translate等命令进行图形构建与变换；④适合高中数学教学与几何作图学习。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(A, C) → i
  8. Polygon(A, B, C) → poly1, c, a_1, b
  9. Polygon(C, B, 3) → poly2, j, k, l, D
  10. Polygon(A, C, 3) → poly3, m, n, p, E
  11. Rotate(A, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → A'
  12. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → C'
  13. Segment(A', C') → i'
  14. Rotate(B, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → B'_1
  15. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → C'_1
  16. Segment(B'_1, C'_1) → h'
  17. Rotate(B'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → I
  18. Rotate(C'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → J
  19. Segment(I, J) → h''
  20. Rotate(A', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → A''
  21. Rotate(C', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → C''
  22. Segment(A'', C'') → i''
  23. Midpoint(E, D) → L
  24. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], L) → D'
  25. Dilate(L, If[5 < d ≤ 6, 6 - d, 0], E) → L'
  26. Rotate(D, If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D'_1
  27. Rotate(D', If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D''
  28. Dilate(A, If[3 < d ≤ 4, 4 - d, 0], D) → A'_1
  29. Segment(A, A'_1) → q
  30. Dilate(D, If[5 < d ≤ 6, 6 - d, 0], B) → D'_2
  31. Vector(D, D'_2) → u
  32. Translate(A, u) → A'_2
  33. Translate(A'_1, u) → F
  34. Segment(A'_2, F) → q'
  35. Line(B, q) → r
  36. Line(E, B) → s
  37. Point(r) → G
  38. Angle(E, B, G) → β
  39. Rotate(A'_2, If[5 < d ≤ 6, ((-(d - 5)) * β), (-β)], D'_2) → H
  40. Rotate(F, If[5 < d ≤ 6, ((-(d - 5)) * β), (-β)], D'_2) → F'
  41. Segment(H, F') → q''