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Parallel Lines Consequences in Coordinate Plane

Parallel Lines Consequences in Coordinate Plane
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2016-10-07 19:27
AngleVectorTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the immediate consequences of parallel lines in the coordinate plane. It involves core math concepts like parallel lines, coordinate geometry, angles, and vectors. Construction highlights include commands like Rotate, Angle, Ray, Line, Point, Circle, Intersect, Segment, Min, Polygon, Dilate, Vector, and Translate from GeoGebra. Suitable for high school students learning coordinate geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(B, (a * π / 180), A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B') → g
  4. Line(A, B') → h
  5. Point(h) → C
  6. Ray(B', C) → i
  7. Point(i) → D
  8. Line(E, h) → j
  9. Circle(D, b) → c
  10. Intersect(c, k, 2) → F
  11. Intersect(h, l) → G
  12. Segment(G, F) → m
  13. Segment(F, D) → n
  14. Min(m, n) → d
  15. Circle(F, (0.3 * d)) → e
  16. Intersect(e, k, 2) → H
  17. Intersect(e, m, 1) → I
  18. Polygon(D, F, G) → poly1, g_1, d_1, f_1
  19. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], F) → G'
  20. Segment(G, G') → r
  21. Dilate(F, If[1 < o ≤ 2, 2 - o, 0], D) → F'
  22. Segment(F, F') → s
  23. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], E) → D'
  24. Vector(D, D') → u
  25. Translate(D, u) → D'_1
  26. Translate(F, u) → F'_1
  27. Translate(G, u) → G'_1
  28. Polygon(D'_1, F'_1, G'_1) → poly1', g'_1, d'_1, f'_1
  29. Translate(G, u) → G'_2
  30. Translate(G', u) → G''
  31. Segment(G'_2, G'') → r'
  32. Translate(F, u) → F'_2
  33. Translate(F', u) → F''
  34. Segment(F'_2, F'') → s'
  35. Segment(D'_1, G'_1) → h_1
  36. Angle(G, F, D) → β
  37. Angle(G'_1, F'_1, D'_1) → γ