平行线上的角 by azb

平行线上的角 by azb
几何画板及绘图内容加载中,请稍等……
2015-01-06 03:08
①本范例演示平行线上的内错角、同位角、同旁内角关系;②涉及核心数学概念包括平行线性质、角相等与互补定理;③构造要点:使用Segment命令绘制线段,Intersect命令求交点,Angle命令测量角度,Point命令标记关键点;④适合初中及以上学生学习平行线几何性质,也可用于高中几何证明辅助教学。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(C, D) → b
  3. Segment(E, F) → c
  4. Intersect(b, c) → G
  5. Intersect(a, c) → H
  6. Angle(b, c) → α
  7. Segment(I_1, J_1) → d_1
  8. Segment(K_1, L_1) → e_1
  9. Segment(M_1, N_1) → f_1
  10. Intersect(d_1, f_1) → O_1
  11. Intersect(e_1, f_1) → P_1
  12. Point(b) → U
  13. Intersect(b, c) → V
  14. Point(a) → W
  15. Point(a) → A_1
  16. Point(b) → B_1
  17. Point(d_1) → C_1
  18. Point(d_1) → D_1
  19. Point(d_1) → E_1
  20. Point(e_1) → F_1
  21. Intersect(e_1, f_1) → G_1
  22. Point(e_1) → H_1
  23. Intersect(a, c) → Z
  24. Angle(A_1, Z, F) → β
  25. Intersect(d_1, f_1) → W_1
  26. Point(d_1) → Z_1
  27. Point(d_1) → A_2
  28. Point(e_1) → B_2
  29. Intersect(e_1, f_1) → C_2
  30. Point(e_1) → D_2
  31. Intersect(b, c) → E_2
  32. Intersect(a, c) → F_2
  33. Intersect(e_1, f_1) → G_2
  34. Point(b) → K_2
  35. Point(a) → L_2
  36. Point(b) → M_2
  37. Point(a) → N_2
  38. Point(d_1) → O_2
  39. Point(e_1) → P_2
  40. Point(e_1) → Q_2
  41. Point(d_1) → R_2
  42. Intersect(d_1, f_1) → H_2
  43. Angle(O_2, H_2, G_2) → γ
  44. Angle(Q_2, G_2, H_2) → δ
  45. Segment(M_3, N_3) → d_2
  46. Segment(O_3, P_3) → e_2
  47. Segment(Q_1, R_1) → f_2
  48. Intersect(d_2, f_2) → S_2
  49. Intersect(e_2, f_2) → T_1
  50. Intersect(d_2, f_2) → Q_3
  51. Point(d_2) → R_3
  52. Intersect(e_2, f_2) → S_3
  53. Point(e_2) → T_2
  54. Point(e_2) → U_1
  55. Point(d_2) → V_2
  56. Intersect(d_2, f_2) → I_2
  57. Intersect(e_2, f_2) → J_2
  58. Point(d_2) → S_1
  59. Point(d_2) → T_3
  60. Point(e_2) → U_2
  61. Point(e_2) → V_1
  62. Angle(J_2, I_2, S_1) → η_1
  63. Angle(V_1, J_2, I_2) → ε_1
  64. Segment(Q, R) → d
  65. Segment(S, T) → e
  66. Angle(e, d) → ε
  67. Intersect(d, e) → W_2
  68. Segment(W_2, Q) → f
  69. Angle(S, W_2, Q) → ζ

AI 绘图提示语参考

绘制两条平行线a和b,以及两条穿过它们的直线c和d。标记它们的交点分别为G、H、O、P、Z、W、V、U。测量角α、β、γ、δ,它们分别是c和d的交角、a和c的交角、d1和f1的交角、e1和f1的交角。
以上提示语为根据原始绘图命令整理而来,仅供参考。