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等腰梯形探究 by atreitman

等腰梯形探究 by atreitman
几何画板及绘图内容加载中，请稍等……
2016-01-25 23:28
多边形向量最值优化几何作图
①本范例演示等腰梯形的几何性质与向量关系；②涉及核心数学概念包括多边形、向量、角度、距离、中点、线性规划等；③构造过程中运用了线段、直线、点、角平分线、镜像、斜率、角度、距离、中点、交点等 GeoGebra 命令与对象；④适合高中数学教学，用于探究几何变换与优化问题。

GeoGebra 命令及参数

  1. Segment(B, A) → a
  2. Line(C_1, a) → b
  3. Point(b) → D
  4. Segment(A, D) → c
  5. LineBisector(a) → d
  6. Mirror(A, d) → A'
  7. Mirror(D, d) → C
  8. Segment(A', C) → c'
  9. Segment(D, C) → e
  10. Slope(a) → m
  11. Slope(e) → m_1
  12. Slope(c) → m_2
  13. Slope(c') → m_3
  14. Angle(A, B, C) → α
  15. Angle(B, C, D) → β
  16. Angle(C, D, A) → γ
  17. Angle(D, A, B) → C_2
  18. Distance(A, B) → distanceAB
  19. Midpoint(A, B) →
  20. Distance(B, C) → distanceBC
  21. Midpoint(B, C) →
  22. Distance(C, D) → distanceCD
  23. Midpoint(C, D) →
  24. Distance(D, A) → distanceDA
  25. Midpoint(D, A) →
  26. Segment(A, C) → i
  27. Segment(B, D) → j
  28. Intersect(i, j) → E
  29. Distance(A, E) → distanceAE
  30. Midpoint(A, E) →
  31. Distance(E, B) → distanceEB
  32. Midpoint(E, B) →
  33. Distance(E, C) → distanceEC
  34. Midpoint(E, C) →
  35. Distance(E, D) → distanceED
  36. Midpoint(E, D) →
  37. Angle(B, E, A) → δ
  38. Angle(A, E, D) → ε
  39. Angle(D, E, C) → ζ
  40. Angle(C, E, B) → η
  41. Angle(B, C, E) → θ
  42. Angle(E, C, D) → ι
  43. Angle(C, D, E) → κ
  44. Angle(E, D, A) → λ
  45. Angle(D, A, E) → μ
  46. Angle(E, A, B) → ν
  47. Angle(A, B, E) → ξ
  48. Angle(E, B, C) → ο