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解析几何：平行四边形的几何性质与构造

解析几何：平行四边形的几何性质与构造
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2015-11-05 22:23
多边形角解析几何几何作图
本范例旨在演示解析几何中平行四边形的几何性质与坐标关系。涉及的核心数学概念包括向量运算、平面几何角度关系以及多边形的基本属性。作图要点在于使用 GeoGebra 软件中的线段、直线、角度、多边形及点命令来精确构建图形结构。该范例适合中学生学习几何知识，或教师用于课堂动态演示，帮助直观理解平行四边形的判定与性质。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(C, D) → b
  3. Segment(A, C) → c
  4. Segment(B, D) → d
  5. Segment(E, B) → e
  6. Segment(E, D) → f
  7. Segment(E, C) → g
  8. Segment(E, A) → h
  9. Line(A, a) → i
  10. Line(D, i) → j
  11. Line(F, c) → k
  12. Angle(E, D, C) → α
  13. Angle(B, D, E) → β
  14. Angle(E, A, B) → γ
  15. Angle(C, A, E) → δ
  16. Angle(D, C, E) → ε
  17. Angle(A, B, E) → ζ
  18. Angle(E, B, D) → η
  19. Angle(E, C, A) → θ
  20. Segment(C, D) → t
  21. Segment(A, C) → a_1
  22. Segment(B, D) → b_1
  23. Segment(A, B) → c_1
  24. Angle(C, A, B) → κ
  25. Angle(B, D, C) → λ
  26. Angle(A, B, D) → μ
  27. Angle(D, C, A) → ν
  28. Segment(B, A) → d_1
  29. Segment(A, D) → e_1
  30. Segment(D, C) → f_1
  31. Segment(C, A) → h_1
  32. Segment(A, D) → i_1
  33. Segment(D, B) → j_1
  34. Segment(A, C) → l_1
  35. Segment(C, B) → m_1
  36. Segment(B, D) → n_1
  37. Segment(A, B) → p_1
  38. Segment(B, C) → q_1
  39. Segment(C, D) → r_1
  40. Segment(A, B) → a_2
  41. Segment(A, C) → b_2
  42. Segment(C, D) → c_2
  43. Segment(D, B) → d_2
  44. Polygon(A, B, D) → poly1, d_3, a_3, b_3
  45. PointIn(poly1) → Pointpoly1
  46. Polygon(A, C, D) → poly2, d_4, a_4, c_3
  47. PointIn(poly2) → Pointpoly2
  48. Polygon(A, C, B) → poly3, b_4, a_5, c_4
  49. Polygon(B, D, C) → poly4, c_5, b_5, d_5
  50. PointIn(poly3) → Pointpoly3
  51. PointIn(poly4) → Pointpoly4