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Corresponding Angles and Parallel Lines

Corresponding Angles and Parallel Lines
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2016-02-05 09:14
AngleVectorGeometric Construction
In collections Geometry: Parallel Lines & Related Angles
This example demonstrates the relationship between corresponding angles and parallel lines. Key mathematical concepts include angles and straight lines. Using GeoGebra commands such as Point, Rotate, Angle, and Line, the construction of corresponding angles on parallel lines is illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, K, I) → g
  13. CircleSector(C, I, J) → h
  14. CircleSector(C, J, H) → k
  15. CircleSector(C, H, K) → p
  16. CircleSector(A, E, G) → q
  17. CircleSector(A, G, D) → r
  18. CircleSector(A, D, F) → s
  19. CircleSector(A, F, E) → t
  20. Dilate(A, If[0 < i < 1, 1 - i, 0], C) → A'
  21. Vector(A, A') → u
  22. Translate(q, u) → q'
  23. Translate(r, u) → r'
  24. Translate(s, u) → s'
  25. Translate(t, u) → t'
  26. CircleArc(A, E, G) → c_1
  27. CircleArc(C, K, I) → d_1
  28. CircleArc(C, I, J) → e_1
  29. CircleArc(A, G, D) → f_1
  30. CircleArc(A, D, F) → g_1
  31. CircleArc(C, J, H) → h_1
  32. CircleArc(A, F, E) → k_1
  33. CircleArc(C, H, K) → p_1