中点平行四边形

中点平行四边形
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2015-12-04 17:55
①本范例演示了通过四边形顶点中点构造平行四边形的现象;②涉及的核心数学概念包括平行四边形、复数、垂心、分段函数、不等式和抛物线;③作图要点——从下方『构造摘要』提炼用到了Polygon(多边形)、Midpoint(中点)等GeoGebra命令和对象;④适合高中数学教学或几何作图学习。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a_{12}, b_{11}, c_{12}, d_{12}
  2. Midpoint(a_{12}) → E
  3. Midpoint(d_{12}) → F
  4. Midpoint(c_{12}) → G
  5. Midpoint(b_{11}) → H
  6. Polygon(A_1, B_1, C_1, D_1) → poly1_1, a_7, b_{10}, c_7, d_7
  7. Midpoint(a_7) → E_1
  8. Midpoint(d_7) → F_1
  9. Midpoint(c_7) → G_1
  10. Midpoint(b_{10}) → H_1
  11. Polygon(A_2, B_2, C_2, D_2) → poly1_2, a_8, b_7, c_8, d_8
  12. Midpoint(a_8) → E_2
  13. Midpoint(d_8) → F_2
  14. Midpoint(c_8) → G_2
  15. Midpoint(b_7) → H_2
  16. Polygon(A_3, B_3, C_3, D_3) → poly1_3, a_9, b_8, c_9, d_9
  17. Midpoint(a_9) → E_3
  18. Midpoint(d_9) → F_3
  19. Midpoint(c_9) → G_3
  20. Midpoint(b_8) → H_3
  21. Polygon(A_4, B_4, C_4, D_4) → poly1_4, a_{10}, b_9, c_{10}, d_{10}
  22. Midpoint(a_{10}) → E_4
  23. Midpoint(d_{10}) → F_4
  24. Midpoint(c_{10}) → G_4
  25. Midpoint(b_9) → H_4
  26. Polygon(A_5, B_5, C_5, D_5) → poly1_5, a_{11}, c, c_{11}, d_{11}
  27. Midpoint(a_{11}) → E_5
  28. Midpoint(d_{11}) → F_5
  29. Midpoint(c_{11}) → G_5
  30. Midpoint(c) → H_5
  31. Polygon(F, G, H, E) → poly2, a_6, b_6, c_6, d_6
  32. Polygon(F_1, G_1, H_1, E_1) → poly2_1, a_5, b_5, c_5, d_5
  33. Polygon(F_2, G_2, H_2, E_2) → poly2_2, b_2, c_2, d_2, a_2
  34. Polygon(F_3, G_3, H_3, E_3) → poly2_3, b_3, c_3, d_3, a_3
  35. Polygon(F_4, G_4, H_4, E_4) → poly2_4, a_4, b_4, c_4, d_4
  36. Polygon(F_5, G_5, H_5, E_5) → poly2_5, b_1, c_1, d_1, a_1