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菱形的旋转对称

菱形的旋转对称
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2019-02-26 07:35
多边形变换几何作图
本范例演示了四边形的旋转对称性，特别是菱形。核心数学概念包括旋转对称和几何作图。通过使用GeoGebra命令如Segment, OrthogonalLine, Point, Intersect, Circle, Line, Polygon, Rotate, Mirror等，可以构造出菱形并展示其旋转对称性。适合初中及以上学生学习几何变换。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Segment(C, B) → e
  8. Segment(D, A) → f
  9. Intersect(e, f) → E
  10. Segment(K, L) → l
  11. Circle(K, L) → p
  12. Point(p) → M
  13. Segment(K, M) → m
  14. Line(M, l) → n
  15. Line(L, m) → q
  16. Intersect(n, q) → N
  17. Segment(M, L) → r
  18. Segment(N, K) → s
  19. Intersect(r, s) → O
  20. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  21. Rotate(C, (-α), E) → C'
  22. Rotate(D, (-α), E) → D'
  23. Rotate(B, (-α), E) → B'
  24. Rotate(A, (-α), E) → A'
  25. Polygon(C', D', B', A') → poly1', c', d', b', a'
  26. Rotate(M, (-α), O) → M'
  27. Rotate(N, (-α), O) → N'
  28. Rotate(L, (-α), O) → L'
  29. Rotate(K, (-α), O) → K'
  30. Polygon(M', N', L', K') → poly3', m', n', l', k'
  31. Segment(P, Q) → t
  32. Segment(P, R) → e_1
  33. Line(Q, e_1) → g_1
  34. Line(R, t) → h_1
  35. Intersect(g_1, h_1) → S
  36. Segment(R, Q) → i_1
  37. Segment(S, P) → j_1
  38. Intersect(i_1, j_1) → T
  39. Rotate(P, (-α), T) → P'
  40. Rotate(R, (-α), T) → R'
  41. Rotate(S, (-α), T) → S'
  42. Rotate(Q, (-α), T) → Q'
  43. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  44. Segment(U, V) → t_1
  45. Line(W, t_1) → b_2
  46. Point(b_2) → Z
  47. Segment(W, V) → d_2
  48. Segment(Z, U) → e_2
  49. Intersect(d_2, e_2) → A_1
  50. Rotate(U, (-α), A_1) → U'
  51. Rotate(V, (-α), A_1) → V'
  52. Rotate(Z, (-α), A_1) → Z'
  53. Rotate(W, (-α), A_1) → W'
  54. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  55. Line(B_1, C_1) → f_2
  56. Mirror(D_1, f_2) → E_1
  57. Segment(D_1, E_1) → g_2
  58. Intersect(f_2, g_2) → F_1
  59. Rotate(D_1, (-α), F_1) → G_1
  60. Rotate(B_1, (-α), F_1) → H_1
  61. Rotate(E_1, (-α), F_1) → I_1
  62. Rotate(C_1, (-α), F_1) → J_1
  63. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  64. Intersect(m, m_1) → H
  65. Intersect(m', k') → I