比较图形

比较图形
几何画板及绘图内容加载中,请稍等……
2014-05-01 23:14
这个范例演示了相似图形的概念。通过使用缩放、旋转等变换,可以观察到相似图形的性质。构造摘要中使用了Polygon, Midpoint, Segment等GeoGebra命令。适合初中及以上学生学习几何变换。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(a) → D
  3. Midpoint(b) → E
  4. Midpoint(c) → F
  5. Segment(F, C) → d
  6. Segment(E, B) → e
  7. Intersect(d, e) → G
  8. Mirror(G, a) → G'
  9. Line(G', a) → f
  10. OrthogonalLine(D, a) → g
  11. Intersect(g, f) → H
  12. Ray(D, H) → h
  13. Point(h) → I
  14. Line(I, a) → i
  15. Segment(D, I) → j
  16. OrthogonalLine(F, c) → k
  17. OrthogonalLine(E, b) → l
  18. Circle(F, j) → p
  19. Circle(E, j) → q
  20. Intersect(p, k, 1) → J
  21. Intersect(q, l, 1) → K
  22. Line(J, c) → m
  23. Line(K, b) → n
  24. Intersect(m, n) → L
  25. Intersect(i, n) → M
  26. Intersect(i, m) → N
  27. Segment(F, J) → r
  28. Segment(E, K) → s
  29. Polygon(L, N, M) → poly2, m_1, l_1, n_1
  30. Polygon(O, P, Q, R) → poly3, o, p_1, q_1, r_1
  31. Segment(R, P) → t
  32. Segment(O, Q) → a_1
  33. Intersect(t, a_1) → S
  34. Midpoint(p_1) → T
  35. Midpoint(q_1) → U
  36. Midpoint(r_1) → V
  37. Midpoint(o) → W
  38. Mirror(S, p_1) → S'
  39. Line(S', p_1) → b_1
  40. OrthogonalLine(T, b_1) → c_1
  41. Intersect(b_1, c_1) → Z
  42. Ray(T, Z) → d_1
  43. Point(d_1) → A_1
  44. Line(A_1, p_1) → e_1
  45. Segment(T, A_1) → f_1
  46. OrthogonalLine(W, o) → g_1
  47. Circle(W, f_1) → h_1
  48. Intersect(h_1, g_1, 1) → B_1
  49. Line(B_1, o) → i_1
  50. Segment(W, B_1) → j_1
  51. Intersect(e_1, i_1) → C_1
  52. OrthogonalLine(V, r_1) → k_1
  53. Circle(V, f_1) → s_1
  54. Intersect(s_1, k_1, 1) → D_1
  55. Line(D_1, r_1) → t_1
  56. Segment(V, D_1) → a_2
  57. Intersect(i_1, t_1) → E_1
  58. OrthogonalLine(U, q_1) → b_2
  59. Circle(U, f_1) → c_2
  60. Intersect(c_2, b_2, 1) → F_1
  61. Line(F_1, q_1) → d_2
  62. Segment(U, F_1) → e_2
  63. Intersect(t_1, d_2) → G_1
  64. Intersect(e_1, d_2) → H_1
  65. Polygon(E_1, C_1, H_1, G_1) → poly4, e_3, c_3, h_2, g_2

AI 绘图提示语参考

绘制两个相似三角形,首先画出三角形ABC,然后通过中点D、E、F构造线段和镜像,接着利用垂直线和圆找到相似三角形的对应点,最后通过镜像和垂直线构造出第二个三角形,并确保两个三角形相似。
以上提示语为根据原始绘图命令整理而来,仅供参考。