积极 AI Logo 积极 AI

等边三角形中的旋转与相似

等边三角形中的旋转与相似
几何画板及绘图内容加载中，请稍等……
2017-11-18 09:13
测试改名0几何作图
该范例演示了一个等边三角形中的旋转与相似变换。核心数学概念包括旋转、相似三角形和几何作图。通过使用GeoGebra命令如Rotate、Dilate和Polygon，可以动态地展示等边三角形在旋转和相似变换下的变化。适合初中及以上学生学习几何变换和相似三角形的相关知识。

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(A, C) → h
  7. Segment(C, B) → i
  8. Polygon(A, B, C) → t1, c, a_1, b
  9. Circle(A, (0.15 * Min[h, f])) → d
  10. Intersect(d, f) → D,
  11. Intersect(d, h) → E,
  12. CircleSector(A, D, E) → e
  13. Rotate(B, π / 3, C) → B'_1
  14. Rotate(C, π / 3, A) → C'
  15. Rotate(B, π / 3, A) → B'_2
  16. Rotate(A, If[0 < j ≤ 1, (j * π / 3), π / 3], A) → A'
  17. Rotate(C, If[0 < j ≤ 1, (j * π / 3), π / 3], A) → C'_1
  18. Segment(A', C'_1) → h'
  19. Rotate(C, If[0 < j ≤ 1, (j * π / 3), π / 3], C) → C'_2
  20. Rotate(B, If[0 < j ≤ 1, (j * π / 3), π / 3], C) → B'_3
  21. Segment(C'_2, B'_3) → i'
  22. Rotate(A, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], C) → A'_1
  23. Rotate(C, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], C) → C'_3
  24. Segment(A'_1, C'_3) → h'_1
  25. Rotate(C, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], B) → C'_4
  26. Rotate(B, If[1 < j ≤ 2, ((-(j - 1)) * π / 3), ((-π)) / 3], B) → B'_4
  27. Segment(C'_4, B'_4) → i'_1
  28. Polygon(A, C, C'_1) → t2, c'_1, a_2, c_1
  29. Polygon(B, B'_3, C) → t3, c_2, b_1, b'_3
  30. Rotate(A, If[2 < j ≤ 3, ((j - 2) * π / 3), π / 3], A) → A'_2
  31. Rotate(B, If[2 < j ≤ 3, ((j - 2) * π / 3), π / 3], A) → B'_5
  32. Segment(A'_2, B'_5) → f'
  33. Rotate(A, If[3 < j ≤ 4, ((-(j - 3)) * π / 3), ((-π)) / 3], B) → A'_3
  34. Rotate(B, If[3 < j ≤ 4, ((-(j - 3)) * π / 3), ((-π)) / 3], B) → B'_6
  35. Segment(A'_3, B'_6) → f'_1
  36. Dilate(C'_1, If[5 < j ≤ 6, 6 - j, 0], B'_5) → F
  37. Vector(C'_1, F) → u
  38. Translate(A'_1, u) → G
  39. Translate(C'_3, u) → H
  40. Segment(G, H) → k
  41. Dilate(C, If[6 < j ≤ 7, 7 - j, 0], C'_1) → C'_5
  42. Vector(C, C'_5) → v
  43. Translate(C'_2, v) → I
  44. Translate(B'_3, v) → J
  45. Segment(I, J) → i''
  46. Polygon(C'_1, C, B'_3, B'_5) → q1, c'_2, c_3, b'_1, b'_5