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Dynamic Demonstration of Triangle Angle Bisectors

Dynamic Demonstration of Triangle Angle Bisectors
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2019-03-07 21:39
TriangleAngleGeometric Construction
This example dynamically illustrates a problem posed by Ed Southall on Twitter. It involves triangles and angle bisectors. Using GeoGebra commands such as Rotate, Ray, Point, etc., a modifiable model of triangle angle bisectors is constructed. Suitable for students at the junior high school level and above to learn about triangle-related concepts.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Ray(B, A') → g
  3. Point(g) → C
  4. Polygon(C, B, A) → t1, a_1, c, b
  5. Ray(B, A) → f
  6. Segment(A, C) → h
  7. Segment(C, B) → i
  8. Rotate(A, (a / 2 * π / 180), B) → A'_1
  9. Angle(A, B, A'_1) → α
  10. Ray(B, A'_1) → j
  11. Point(f) → D
  12. Angle(D, A, C) → β
  13. Rotate(D, β / 2, A) → D'
  14. Angle(D, A, D') → γ
  15. Ray(A, D') → k
  16. Intersect(j, k) → E
  17. Angle(B, C, A) → δ
  18. Angle(B, E, A) → ε
  19. Segment(B, A) → l
  20. Min({i, h, l}) → e
  21. Circle(B, (0.2 * e)) → p
  22. Circle(A, (0.2 * e)) → q
  23. Circle(E, (0.2 * e)) → r
  24. Ray(B, A) → m
  25. Intersect(p, m, 1) → F
  26. Intersect(q, m, 2) → G
  27. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], E) → B'
  28. Segment(B, B') → n
  29. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], E) → A'_2
  30. Segment(A, A'_2) → s
  31. Rotate(F, If[1 < d ≤ 2, ((d - 1) * α), α], B) → E'
  32. CircleSector(B, F, E') → t
  33. Rotate(t, If[3 < d ≤ 4, ((d - 3) * α), α], B) → t'
  34. Rotate(G, If[4 < d ≤ 5, ((d - 4) * γ), γ], A) → G'
  35. CircleSector(A, G, G') → c_1
  36. Rotate(c_1, If[6 < d ≤ 7, ((d - 6) * γ), γ], A) → d_1
  37. Intersect(r, n, 1) → I
  38. Rotate(I, If[7 < d ≤ 8, ((d - 7) * ε), ε], E) → I'
  39. CircleSector(E, I, I') → e_1
  40. Dilate(E, If[9 < d ≤ 10, 10 - d, 0], C) → E'_1
  41. Vector(E, E'_1) → u
  42. Translate(e_1, u) → f_1
  43. Line(E, i) → g_1
  44. Point(g_1) → H
  45. Angle(B, E, H) → ζ
  46. Rotate(f_1, If[9 < d ≤ 10, ((d - 9) * ζ), ζ], E'_1) → h_1
  47. Rotate(I, If[10 < d ≤ 11, ((d - 10) * ε), ε], E) → I'_2
  48. CircleSector(E, I, I'_2) → k_1
  49. Semicircle(E, C) → p_1
  50. Midpoint(E, C) → J
  51. Rotate(E, If[12 < d ≤ 13, ((-(d - 12)) * π), (-π)], J) → E'_2
  52. Vector(E, E'_2) → v
  53. Translate(k_1, v) → q_1
  54. Rotate(B, δ / 2, C) → B'_1
  55. Ray(C, B'_1) → i_1
  56. Line(E, i_1) → j_1
  57. Intersect(r, j_1, 2) → K
  58. Angle(K, E, I) → η
  59. Rotate(q_1, If[12 < d ≤ 13, ((-(d - 12)) * η), (-η)], E'_2) → r_1