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Alternate Angle Bisector Construction

Alternate Angle Bisector Construction
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2019-07-03 20:31
CircleAngleGeometric Construction
This example demonstrates the construction of an angle bisector using an alternative compass-and-straightedge method. It involves core mathematical concepts such as angles, geometric constructions, and the application of compass and straightedge tools. Key GeoGebra commands and objects used include Intersect, Ray, Rotate, Angle, Circle, CircleSector, Segment, Point, CircleArc, and Dilate. Suitable for high school mathematics education or for enthusiasts of geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Ray(A, B) → f
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → β
  5. Ray(A, B') → g
  6. Circle(A, 1) → c
  7. Rotate(B, α / 2, A) → B'_1
  8. Angle(B, A, B'_1) → γ
  9. Ray(A, B'_1) → h
  10. Intersect(c, h, 1) → C
  11. Intersect(c, f, 1) → D
  12. CircleSector(A, D, C) → d
  13. Intersect(c, g, 1) → E
  14. CircleSector(A, D, E) → e
  15. Circle(A, a) → k
  16. Circle(A, b) → p
  17. Intersect(k, f, 1) → F
  18. Intersect(k, g, 1) → G
  19. Intersect(p, f, 1) → H
  20. Intersect(p, g, 1) → I
  21. Segment(F, I) → i
  22. Segment(H, G) → j
  23. Intersect(h, i) → J
  24. Point(h) → K
  25. Ray(J, K) → l
  26. CircleSector(A, H, I) → q
  27. Rotate(F, If[0 < m ≤ 1, (m * α), α], A) → F'
  28. CircleArc(A, F, F') → r
  29. Rotate(H, If[1 < m ≤ 2, ((m - 1) * α), α], A) → H'
  30. CircleArc(A, H, H') → s
  31. Dilate(F, If[2 < m ≤ 3, 3 - m, 0], I) → F'_1
  32. Segment(F, F'_1) → n
  33. Dilate(H, If[3 < m ≤ 4, 4 - m, 0], G) → H'_1
  34. Segment(H, H'_1) → t
  35. Dilate(A, If[5 < m ≤ 6, 6 - m, 0], J) → A'
  36. Segment(A, A') → f_1
  37. Rotate(d, If[7 < m ≤ 8, ((m - 7) * α / 2), α / 2], A) → d'