平行四边形的对称轴 by سید مهدی بشارت

平行四边形的对称轴 by سید مهدی بشارت
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2016-06-09 02:21
①本范例演示平行四边形的对称轴及其性质;②涉及核心数学概念包括对称性、平行四边形性质、中点、旋转与镜像变换;③作图要点运用了PointIn, Polygon, Midpoint, Line, Circle, Intersect, Rotate, Mirror等GeoGebra命令与对象;④适合初中及以上学生学习几何变换与对称性,也可用于高中数学教学。

GeoGebra 命令及参数

  1. PointIn(j) → B
  2. PointIn(j) → D
  3. PointIn(j) → C
  4. PointIn(j) → A
  5. Polygon(A, B, C, D) → poly1, a, b, c, d
  6. Midpoint(a) → E
  7. Midpoint(c) → F
  8. Midpoint(d) → G
  9. Midpoint(b) → H
  10. Line(E, F) → f
  11. Line(G, H) → g
  12. Line(A, C) → h
  13. Line(D, B) → i_2
  14. Circle(H, 1, xOyPlane) → e
  15. Circle(B, 1, xOyPlane) → k
  16. Circle(E, 1, xOyPlane) → p
  17. Circle(C, 1, xOyPlane) → q
  18. Intersect(f, p, 1) → I
  19. Intersect(i_2, k, 2) → J
  20. Intersect(g, e, 2) → K
  21. Intersect(h, q, 2) → L
  22. Circle(I, 0.5, f) → r
  23. Circle(J, 0.5, i_2) → s
  24. Circle(K, 0.5, g) → t
  25. Circle(L, 0.5, h) → c_1
  26. Polygon(E, A, D, F) → poly2, e_1, a_1, d_1, f_1
  27. Polygon(E, B, C, F) → poly3, e_2, b_1, c_2, f_2
  28. Rotate(B, α, f) → B'
  29. Rotate(C, α, f) → C'
  30. Polygon(F, C', B', E) → poly4, f_3, c', b', e_3
  31. Polygon(G, D, C, H) → poly6, g_1, d_2, c_3, h_1
  32. Polygon(H, B, A, G) → poly7, h_2, b_2, a_2, g_2
  33. Rotate(C, (-α), g) → C'_1
  34. Rotate(D, (-α), g) → D'
  35. Polygon(D', G, H, C'_1) → poly8, d', g_3, h_3, c'_1
  36. Polygon(D, A, B) → poly9, b_3, d_3, a_3
  37. Polygon(D, B, C) → poly10, c_4, d_4, b_4
  38. Rotate(C, (-α), i_2) → C'_2
  39. Intersect(b, a) → Q
  40. Polygon(C'_2, B, D) → poly11, d_5, c'_2, b_5
  41. Polygon(A, B, C) → poly12, c_5, a_4, b_6
  42. Polygon(A, C, D) → poly13, d_6, a_5, c_6
  43. Rotate(D, (-α), h) → D'_1
  44. Polygon(D'_1, A, C) → poly14, c_7, d'_1, a_6
  45. Intersect(g, f) → R
  46. Intersect(i_2, h) → S
  47. Mirror(S, B) → S'
  48. Mirror(S, C) → S'_1
  49. Mirror(R, H) → R'
  50. Mirror(R, E) → R'_1
  51. Circle(R'_1, 0.25, xOyPlane) → k_1
  52. Circle(S', 0.25, xOyPlane) → p_1
  53. Circle(R', 0.25, xOyPlane) → q_1
  54. Circle(S'_1, 0.25, xOyPlane) → r_1
  55. Mirror(L, G) → L'
  56. Polygon(L', T, 4, xOyPlane) → poly15, i_1, j_1, l_1, m_1, U, V

AI 绘图提示语参考

画一个平行四边形,标出它的对角线和中点,然后画出通过中点的对称轴。以其中一条对角线为轴,将平行四边形旋转180度,观察旋转后的图形与原图重合。再以另一条对角线为轴,将平行四边形旋转180度,同样观察旋转后的图形与原图重合。最后,画出两条对角线交点处的圆,并标注关键点和线段,展示平行四边形的对称性和旋转变换特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。