中点与四边形

中点与四边形
几何画板及绘图内容加载中,请稍等……
2016-07-11 14:54
本范例通过连接正方形顶点和对边中点的线段,形成一个四边形。演示了四边形的构造方法,涉及正方形和中点的概念。使用了Segment, OrthogonalLine, Circle, Intersect, Midpoint, Polygon, Rotate等GeoGebra命令。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Circle(B, A) → c
  4. Intersect(c, b, 2) → C
  5. OrthogonalLine(C, b) → d
  6. Circle(C, B) → e
  7. Intersect(e, d, 2) → D
  8. Segment(B, C) → f
  9. Segment(D, C) → g
  10. Segment(A, D) → h
  11. Midpoint(a) → E
  12. Midpoint(f) → F
  13. Midpoint(g) → G
  14. Midpoint(h) → H
  15. Segment(A, F) → i
  16. Segment(H, C) → j
  17. Segment(E, D) → k
  18. Segment(B, G) → l
  19. Intersect(i, k) → I
  20. Intersect(i, l) → J
  21. Intersect(j, l) → K
  22. Intersect(j, k) → L
  23. Polygon(A, I, L, H) → poly1, a_1, i_1, l_1, h_1
  24. Polygon(I, J, K, L) → poly2, i_2, j_1, k_1, l_2
  25. Polygon(E, B, J, I) → poly3, e_1, b_1, j_2, i_3
  26. Polygon(E, I, A) → poly4, a_2, e_2, i_4
  27. Polygon(H, L, D) → poly5, d_1, h_2, l_3
  28. Polygon(L, K, G, D) → poly6, l_4, k_2, g_1, d_2
  29. Polygon(B, F, J) → poly7, j_3, b_2, f_1
  30. Polygon(J, F, C, K) → poly8, j_4, f_2, c_1, k_3
  31. Rotate(H, (-α), D) → H'
  32. Rotate(L, (-α), D) → L'
  33. Rotate(D, (-α), D) → D'
  34. Polygon(H', L', D') → poly5', d', h', l'
  35. Rotate(G, (-α), C) → G'
  36. Rotate(K, (-α), C) → K'
  37. Rotate(C, (-α), C) → C'
  38. Polygon(G', K', C') → poly9', c', g', k'
  39. Rotate(B, (-α), B) → B'
  40. Rotate(F, (-α), B) → F'
  41. Rotate(J, (-α), B) → J'
  42. Polygon(B', F', J') → poly7', j', b', f'
  43. Rotate(E, (-α), A) → E'
  44. Rotate(I, (-α), A) → I'
  45. Rotate(A, (-α), A) → A'
  46. Polygon(E', I', A') → poly4', a', e', i'