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Parallel Lines Coordinate Demo

Parallel Lines Coordinate Demo
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2018-03-04 09:18
VectorCoordinate GeometryGeometric Construction
In collections A1.ACE.1 - Create and solve equations and inequalities Slope
This example demonstrates the dynamic and modifiable properties of parallel lines in the coordinate plane. It involves core math concepts like parallel line properties, coordinate geometry, and angle measurement. Construction highlights include commands like Rotate, Angle, Line, Point, Circle, Intersect, Segment, Min, Polygon, Dilate, Vector, and Translate. Suitable for high school mathematics teaching, helping students understand and apply theorems related to parallel lines and geometric constructions.

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