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Angle Bisector Locus Construction

Angle Bisector Locus Construction
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2012-05-30 15:14
AngleGeometric ConstructionLocus
This example demonstrates the geometric construction of the angle bisector locus. The key mathematical concepts include angle bisectors, loci, and geometric construction. The construction involves GeoGebra commands such as Line, AngularBisector, Intersect, and others. It is suitable for middle or high school geometry learning to understand the properties and construction of angle bisectors.

GeoGebra Commands & Parameters

  1. Line(A, B) → a_1
  2. Line(C, D) → b_1
  3. AngularBisector(a_1, b_1) → c, d
  4. Intersect(a_1, b_1) → E
  5. Point(d) → F_1
  6. Angle(F_1, E, A) → α
  7. Angle(D, E, F_1) → β
  8. Point(d) → G_1
  9. OrthogonalLine(G_1, a_1) → e
  10. OrthogonalLine(G_1, b_1) → f
  11. Intersect(e, a_1) → H_1
  12. Intersect(f, b_1) → I
  13. Segment(G_1, I) → a_2
  14. Segment(H_1, G_1) → b_2
  15. Distance(a_2, b_2) → i
  16. OrthogonalLine(F, b_1) → g
  17. OrthogonalLine(F, a_1) → h
  18. Intersect(g, b_1) → G
  19. Intersect(h, a_1) → H
  20. Segment(H, F) → a
  21. Segment(F, G) → b
  22. Distance(F, H) → distanceFH
  23. Distance(G, F) → distanceGF
  24. Angle(B, H, F) → γ
  25. Angle(D, G, F) → δ
  26. Intersect(c, b_1) → J
  27. Point(c) → K
  28. Angle(K, J, G) → ε
  29. Angle(B, J, K) → ζ
  30. Point(c) → L
  31. Angle(L, J, D) → η

AI Drawing Prompt Reference

Draw two sides of an angle and its bisector. Take a point on the bisector, connect it to the sides of the angle, and draw perpendiculars from this point to each side. Observe the lengths of the segments formed by connecting the feet of the perpendiculars to the point on the bisector. Repeat the process with another point on the bisector to show the locus of such points.
The prompt above was compiled from the original drawing commands and is for reference only.