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Parallel Line Puzzle

Parallel Line Puzzle
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2016-04-28 03:23
Coordinate GeometryCalculusGeometric Construction
This example demonstrates the geometric properties of parallel lines and intersection calculations. Core math concepts include straight lines, subtraction, integral calculus, orthocenter, terms, and scatter plots. Construction highlights involve commands like Random, Segment, Intersect, If, Line, OrthogonalLine, LineBisector in GeoGebra. Suitable for high school and above students exploring geometric constructions and calculus applications.

GeoGebra Commands & Parameters

  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