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平行四边形与相关几何变换动画

平行四边形与相关几何变换动画
几何画板及绘图内容加载中，请稍等……
2017-02-10 05:56
多边形三角函数变换几何作图
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
①本范例通过动画演示平行四边形的构造及其变换；②涉及核心数学概念包括平行四边形性质、相似三角形、单位圆、椭圆、变换（旋转、平移、缩放）；③构造要点：运用了 Rotate（旋转）、Angle（角度）、Ray（射线）、Line（直线）、Point（点）、Intersect（交点）、Segment（线段）、Min（最小值）、Circle（圆）、Dilate（缩放）、Vector（向量）、Polygon（多边形）、Translate（平移）、Midpoint（中点）、CircleSector（扇形）等 GeoGebra 命令；④适合高中数学教学，用于理解几何变换与图形性质。

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(B, If[0 < o ≤ 1, 1 - o, 0], A) → A'
  29. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  30. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], C) → A'_1
  31. Vector(A, A'_1) → u
  32. Segment(A, A'_1) → f_1
  33. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'
  34. Vector(C, C') → v
  35. Segment(C, C') → g_1
  36. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'
  37. Segment(D, D') → h_1
  38. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  39. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  40. Vector(A, A'_2) → w
  41. Translate(A, w) → A'_3
  42. Translate(A', w) → A''
  43. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  44. Vector(A, A'_4) → u_1
  45. Translate(A, u_1) → A'_5
  46. Translate(A'_1, u_1) → L
  47. Intersect(d, i) → M, N
  48. Intersect(d, g) → O, P
  49. Angle(A, C, N) → β
  50. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  51. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  52. Vector(C, C'_1) → v_1
  53. Midpoint(A, D) → Q
  54. Dilate(A, If[4.5 < o ≤ 5.5, 5.5 - o, 0], Q) → A'_6
  55. Segment(A, A'_6) → i_1
  56. Dilate(Q, If[5.5 < o ≤ 6.5, 6.5 - o, 0], D) → Q'
  57. Segment(Q, Q') → j_1
  58. Dilate(B, If[6.5 < o ≤ 7.5, 7.5 - o, 0], Q) → B'_1
  59. Segment(B, B'_1) → k_1
  60. Dilate(Q, If[7.5 < o ≤ 8.5, 8.5 - o, 0], C) → Q'_1
  61. Segment(Q, Q'_1) → l_1
  62. Rotate(A, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], Q) → A'_7
  63. Rotate(A'_6, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → R
  64. Segment(A'_7, R) → m_1
  65. Rotate(B, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → B'_2
  66. Rotate(B'_1, If[10.5 < o ≤ 11.5, ((-(o - 10.5)) * π), (-π)], Q) → S
  67. Segment(B'_2, S) → n_1
  68. Line(A, B) → p_1
  69. Intersect(e, p_1) → T, U
  70. Ray(A, T) → q_1
  71. Intersect(e, f_1) → V,
  72. Intersect(d, i, 1) → W
  73. Ray(C, W) → r_1
  74. Segment(B, A') → t
  75. Rotate(V, If[11 < o ≤ 12, ((o - 11) * (π - α)), π - α], A) → V'
  76. CircleSector(A, V, V') → c_1
  77. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], C) → A'_8
  78. Vector(A, A'_8) → w_1
  79. Translate(c_1, w_1) → d_1
  80. Dilate(C, If[13 < o ≤ 14, 14 - o, 0], D) → C'_2
  81. Vector(C, C'_2) → e_1
  82. Translate(d_1, e_1) → s_1