积极 AI Logo 积极 AI

平行线谜题

平行线谜题
几何画板及绘图内容加载中，请稍等……
2016-04-28 03:23
解析几何微积分几何作图
①本范例演示了平行线的几何性质与交点计算；②涉及的核心数学概念包括直线、减法、积分、垂心、术语、散点图；③作图要点：使用了Random, Segment, Intersect, If, Line, OrthogonalLine, LineBisector等GeoGebra命令与对象；④适合高中及以上数学学习者，用于探索几何构造与微积分应用。

GeoGebra 命令及参数

  1. Random(y(U), y(V)) → newby
  2. Random(x(U), x(Z)) → newbx
  3. Random(x(U), x(Z)) → newax
  4. Random(y(U), y(V)) → neway
  5. Segment(A, B) → a
  6. Segment(C, D) → b
  7. Segment(C, E) → c
  8. Segment(E, F) → d
  9. Segment(D, F) → e
  10. Segment(G, H) → f
  11. Intersect(b, c) → I
  12. Segment(G, K) → i
  13. Intersect(d, e) → L
  14. Segment(L, G) → j
  15. Intersect(c, d) → J
  16. Segment(J, G) → h
  17. If(x(H) - x(G) ≟ 0, 1000, (y(H) - y(G)) / (x(H) - x(G))) → gradblack
  18. If(x(B) - x(A) ≟ 0, 1000, (y(B) - y(A)) / (x(B) - x(A))) → gradred
  19. Line(A, M) → g
  20. OrthogonalLine(B, g) → k
  21. Segment(N, O) → l
  22. Segment(P, Q) → m
  23. Line(A, l) → n
  24. Line(B, m) → p
  25. Intersect(n, p) → R
  26. LineBisector(R, A) → q
  27. LineBisector(B, R) → r
  28. Intersect(p, r) → S
  29. Intersect(n, q) → T
  30. Segment(A, R) → s
  31. Segment(R, B) → t
  32. Segment(U, V) → a_1
  33. Segment(W, V) → b_1
  34. Segment(W, Z) → c_1
  35. Segment(U, Z) → d_1
  36. If(gradred - gradblack ≟ 0, 1, 0) → Parallel
  37. If(gradred - gradblack ≟ 0, 1, 0) → correct