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平行四边形与等边三角形组合的旋转动画

平行四边形与等边三角形组合的旋转动画
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2016-10-16 11:06
角向量变换几何作图滑块动画
所属专题 Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
该范例展示了一个由平行四边形、等边三角形和长方体等元素构成的动态几何动画，通过旋转和向量平移等操作呈现图形间的变换关系。核心数学概念包括角度、平行四边形性质、等边三角形、向量以及二维图形与立体图形的关联。作图要点：使用GeoGebra的Rotate、Angle、Ray、Line、Point、Intersect、Segment、Min、Circle、Dilate、CircleSector、Vector、Translate、Polygon等命令，构建了多个点、线段、圆、扇形和多边形对象，并通过滑块或动画控制旋转角度α，观察图形动态变化。适合中学几何教学，用于帮助学生理解旋转、平移、向量和特殊三角形的性质，也可作为动态几何探究的示例。

GeoGebra 命令及参数

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  29. Segment(A, A') → t
  30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  31. CircleSector(A, E, E') → c_1
  32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(c_1, u) → d_1
  35. Segment(A, A'_1) → f_1
  36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  37. Vector(C, C') → v
  38. Translate(d_1, v) → e_1
  39. Segment(C, C') → g_1
  40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  41. Segment(D, D') → h_1
  42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  44. Vector(A, A'_2) → w
  45. Translate(A, w) → A'_3
  46. Translate(A', w) → A''
  47. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  48. Vector(A, A'_4) → u_1
  49. Translate(A, u_1) → A'_5
  50. Translate(A'_1, u_1) → L
  51. Intersect(d, i) → M, N
  52. Intersect(d, g) → O, P
  53. Angle(A, C, N) → β
  54. Rotate(e_1, If[5.5 < o ≤ 6.5, ((-(o - 5.5)) * π), (-π)], D) → k_1
  55. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  56. CircleSector(C, N', N) → p_1
  57. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  58. Vector(C, C'_1) → v_1
  59. Translate(p_1, v_1) → q_1
  60. Rotate(q_1, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], B) → r_1