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Triangle Angle Bisectors

Triangle Angle Bisectors
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2018-02-26 17:26
TriangleAngleGeometric Construction
This example demonstrates the properties and construction of angle bisectors in a triangle. It involves core concepts like the angle bisector theorem, angles, segments, and circles. Key GeoGebra commands used include Polygon, Rotate, Segment, CircleArc, Line, AngularBisector, Intersect, and Midpoint, making it suitable for middle school and above students exploring geometric constructions and properties.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Polygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e
  3. Polygon(B, E, D) → driehoek1, d_1, b_2, e_1
  4. Rotate(B, (((s - 1) * 180))°, d_1) → B'
  5. Rotate(E, (((s - 1) * 180))°, d_1) → E'
  6. Rotate(D, (((s - 1) * 180))°, d_1) → D'
  7. Polygon(B', E', D') → driehoek1', d', b', e'
  8. Rotate(B, 180°, d_1) → B'_1
  9. Rotate(E, 180°, d_1) → E'_1
  10. Rotate(D, 180°, d_1) → D'_1
  11. Polygon(B'_1, E'_1, D'_1) → driehoek1'_1, d'_1, b'_1, e'_1
  12. Segment(B, E) → f
  13. Rotate(D, -90°, B) → DD
  14. CircleArc(B, DD, D) → g
  15. Segment(A, E) → h
  16. Rotate(C, -135°, E) → C'
  17. CircleArc(E, C', C, xOyPlane) → k
  18. Polygon(A, C, E) → driehoek2, e_2, a_2, c_2
  19. Rotate(A, (((s - 3) * 180))°, h) → A'
  20. Rotate(C, -180°, h) → C'_1
  21. Rotate(E, (((s - 3) * (-180)))°, h) → E'_2
  22. Polygon(A, C'_1, E) → driehoek2', p, q, t
  23. Polygon(D'_1, A, E) → driehoek3, e_3, d'_2, a_3
  24. Polygon(A, C, E, DD) → vierhoek3, i, j, l, m
  25. Line(D'_1, E) → n
  26. AngularBisector(A, B, E) → r
  27. Intersect(p, b'_1) → F
  28. Segment(F, E) → g_1
  29. Segment(DD, F) → f_1
  30. Midpoint(A, E) → BB
  31. Angle(E, DD, B) → α
  32. Angle(A, C'_1, E, xOyPlane) → β
  33. Angle(E, BB, B) → γ
  34. Segment(B, BB) → h_1
  35. Segment(A, C'_1) → i_1
  36. Segment(DD, E) → j_1
  37. Angle(E, DD, B) → δ
  38. Angle(A, C'_1, E, xOyPlane) → ε
  39. Angle(E, BB, B) → ζ
  40. AngularBisector(E, A, B) → k_1
  41. AngularBisector(B, E, A) → l_1
  42. Intersect(k_1, d') → J
  43. Intersect(b, e'_1) → K
  44. Intersect(l_1, b) → L
  45. Intersect(k_1, l_1) → M
  46. Segment(E, L) → m_1
  47. Segment(A, J) → n_1