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Angle Bisector Construction by Sara Delgado Rivero

Angle Bisector Construction by Sara Delgado Rivero
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2019-10-08 16:50
AngleTransformationGeometric Construction
This example demonstrates the geometric construction of an angle bisector. It involves core math concepts like angles, segments, circles, intersections, and vectors. The construction uses commands such as Angle, Segment, Point, Circle, Intersect, CircleArc, Ray, OrthogonalLine, Vector, and Translate in GeoGebra. Suitable for middle school and above students learning geometric constructions and properties of angle bisectors.

GeoGebra Commands & Parameters

  1. Angle(A_1, O, C_1) → α
  2. Segment(A_1, O) → a
  3. Segment(O, C_1) → b
  4. Point(b) → A
  5. Circle(O, A) → c
  6. Intersect(c, a, 1) → B
  7. CircleArc(O, B, A) → d
  8. Circle(B, A) → e
  9. Circle(A, B) → f
  10. Intersect(f, e) → C, F, ,
  11. Ray(O, C) → g
  12. Circle(C, 0.6) → h
  13. Intersect(f, h) → G, H, ,
  14. Intersect(h, e) → I, J, ,
  15. CircleArc(B, I, A) → k
  16. CircleArc(A, B, G) → p
  17. Point(g) → P
  18. OrthogonalLine(P, b) → i
  19. OrthogonalLine(P, a) → j
  20. Intersect(b, i) → D
  21. Intersect(j, a) → E
  22. Segment(D, P) → l
  23. Segment(E, P) → m
  24. Circle(D, 0.7) → q
  25. Circle(E, 0.7) → r
  26. Intersect(q, b) → K, L
  27. Intersect(r, a) → M, N
  28. Intersect(r, m) → O_1,
  29. Intersect(q, l) → Q,
  30. Angle(M, E, O_1) → β
  31. Angle(Q, D, L) → γ
  32. Vector(A, B) → u
  33. Translate(A, Vector[(u * n)]) → B'
  34. Ray(O, B') → s
  35. Intersect(d, s) → R,
  36. CircleArc(O, R, A) → t
  37. Vector(A, I) → v
  38. Translate(A, Vector[(v * (n - 1))]) → B'_1
  39. Ray(B, B'_1) → a_1
  40. Intersect(k, a_1) → S,
  41. CircleArc(B, S, A) → c_1
  42. Vector(G, B) → w
  43. Translate(G, Vector[(w * (n - 2))]) → G'
  44. Ray(O, G') → b_1
  45. Intersect(p, b_1) → T,
  46. CircleArc(A, T, G) → d_1
  47. Circle(P, 2) → e_1
  48. Point(g) → U
  49. Vector(O, U) → z
  50. Translate(O, Vector[(z * (n - 3))]) → V'
  51. Segment(O, V') → f_1

AI Drawing Prompt Reference

Draw an angle bisector by starting with two line segments forming an angle and their vertex. Create a circle centered at the vertex that intersects both segments. Connect the intersection points to the vertex. Then, draw two circles centered at the intersection points and find their intersections. Connect the vertex to these intersection points to form the angle bisector. Finally, draw circles centered at the intersection points and find their intersections with the angle bisector to complete the construction.
The prompt above was compiled from the original drawing commands and is for reference only.