探索平行线与截线的变换

探索平行线与截线的变换
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2019-02-16 09:56
本范例通过平移变换探索平行线与截线的性质。演示了平行线与截线的几何关系,涉及的核心数学概念包括平行线、截线及其交点。使用了Line, Point, Circle, Intersect, If等GeoGebra命令进行构造。适合初中及以上学生学习几何变换。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Point(f) → D
  4. Line(D, C) → h
  5. Circle(C, 0.5) → d
  6. Circle(D, 0.5) → c
  7. Intersect(c, f) → E, F
  8. Intersect(c, h) → G, H
  9. Intersect(d, h) → I, J
  10. Intersect(d, g) → K, L
  11. Intersect(i, f) → M
  12. Intersect(i, g) → N
  13. If(y(N) > y(M), CircleSector[C, I, L], CircleSector[C, J, L]) → t
  14. If(y(N) > y(M), CircleSector[C, K, I], CircleSector[C, K, J]) → s
  15. If(y(N) > y(M), CircleSector[C, J, K], CircleSector[C, I, K]) → r
  16. If(y(N) > y(M), CircleSector[D, F, H], CircleSector[D, F, G]) → q
  17. If(y(N) > y(M), CircleSector[D, G, F], CircleSector[D, H, F]) → p
  18. If(y(N) > y(M), Angle[E, D, G], Angle[E, D, H]) → α
  19. If(y(N) > y(M), Angle[H, D, E], Angle[G, D, E]) → β
  20. If(y(N) > y(M), Angle[F, D, H], Angle[F, D, G]) → γ
  21. If(y(N) > y(M), Angle[G, D, F], Angle[H, D, F]) → δ
  22. If(y(N) > y(M), Angle[J, C, K], Angle[I, C, K]) → ε
  23. If(y(N) > y(M), CircleSector[D, E, G], CircleSector[D, E, H]) → k
  24. If(y(N) > y(M), CircleSector[D, H, E], CircleSector[D, G, E]) → e
  25. If(y(N) > y(M), CircleSector[C, L, J], CircleSector[C, L, I]) → c_1
  26. If(y(N) > y(M), Angle[K, C, I], Angle[K, C, J]) → ζ
  27. If(y(N) > y(M), Angle[I, C, L], Angle[J, C, L]) → η
  28. If(y(N) > y(M), Angle[L, C, J], Angle[L, C, I]) → θ