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平行四边形中的几何变换

平行四边形中的几何变换
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2017-09-13 18:50
多边形变换几何作图
该范例展示了平行四边形中的几何变换问题。核心数学概念包括变换、旋转和平移。通过使用GeoGebra命令如Rotate、Translate和Dilate等，可以动态地演示这些变换。适合初中及以上学生学习几何变换和相关概念。

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(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  55. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  56. Vector(C, C'_1) → v_1
  57. Ray(A, B) → q_1
  58. LineBisector(B, A) → r_1
  59. Distance(C, B) → distanceCB
  60. Segment(C, D) → i_1
  61. Point(i_1) → Q
  62. Line(A, D) → j_1
  63. Line(Q, j_1) → k_1
  64. Line(B, Q) → l_1
  65. Line(C, A) → m_1
  66. Intersect(m_1, k_1) → R
  67. Segment(Q, R) → n_1
  68. Intersect(e, j_1) → S, T
  69. Intersect(e, m_1) → U, V
  70. Line(B, R) → p_1
  71. Intersect(j_1, l_1) → W
  72. Intersect(j_1, p_1) → Z
  73. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], Z) → A'_6
  74. Segment(A, A'_6) → s_1
  75. Dilate(Z, If[7 < o ≤ 8, 8 - o, 0], W) → Z'
  76. Segment(Z, Z') → t_1
  77. Dilate(B, If[7 < o ≤ 8, 8 - o, 0], W) → B'_1
  78. Segment(B, B'_1) → f_2
  79. Dilate(W, If[8 < o ≤ 9, 9 - o, 0], D) → W'
  80. Dilate(W, If[8 < o ≤ 9, 9 - o, 0], Q) → W'_1
  81. Segment(W, W') → g_2
  82. Segment(W, W'_1) → h_2
  83. Dilate(Q, If[9 < o ≤ 10, 10 - o, 0], R) → Q'
  84. Segment(Q, Q') → i_2
  85. Angle(D, A, C) → γ
  86. Rotate(T, If[10 < o ≤ 11, ((o - 10) * γ), γ], A) → T'
  87. CircleSector(A, T, T') → e_2
  88. Dilate(A, If[11 < o ≤ 12, 12 - o, 0], R) → A'_7
  89. Vector(A, A'_7) → w_1
  90. Translate(e_2, w_1) → k_2
  91. Dilate(B, If[12 < o ≤ 13, 13 - o, 0], Z) → B'_2
  92. Segment(B, B'_2) → j_2
  93. Dilate(Z, If[13 < o ≤ 14, 14 - o, 0], R) → Z'_1
  94. Segment(Z, Z'_1) → l_2
  95. Midpoint(A, D) → A_1
  96. Rotate(W, If[15 < o ≤ 16, ((o - 15) * π), π], A_1) → W'_2
  97. Rotate(W', If[15 < o ≤ 16, ((o - 15) * π), π], A_1) → W''
  98. Segment(W'_2, W'') → m_2