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Triangle Angle Bisector Theorem Exploration

Triangle Angle Bisector Theorem Exploration
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2016-04-07 20:24
TriangleAngleGeometric Construction
This applet helps students explore the Triangle Angle Bisector Theorem: if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides. Key concepts include triangles, angle bisectors, and proportions. Using GeoGebra commands such as Line, Ray, Segment, and Polygon, students can visually understand the theorem. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → a_4
  2. Slope(a_4) → b_3
  3. Intersect(a_4, x = 0) → C_1
  4. PointIn(d_4) → C
  5. Segment(A, C) → b
  6. Segment(B, C) → a
  7. Segment(A, B) → g
  8. Polygon(A, B, C) → poly1, d_1, a_1, b_1
  9. Angle(A, C, B) → α
  10. Rotate(A, α / 2, C) → A'
  11. Angle(A, C, A') → β
  12. Ray(C, A') → h
  13. Intersect(h, g) → D
  14. Dilate(C, If[0 < i ≤ 1, 1 - i, 0], D) → D'
  15. Segment(C, D') → j
  16. Circle(C, (0.2 * j)) → k
  17. Intersect(k, b) → F, K
  18. Intersect(k, j) → G,
  19. CircleSector(C, F, G) → p
  20. Rotate(p, If[1.5 < i ≤ 2.5, ((i - 1.5) * β), β], C) → p'
  21. Segment(A, D) → c_1
  22. Segment(D, B) → c_2
  23. Ray(A, C) → n
  24. Line(B, j) → q
  25. Intersect(q, n) → E
  26. Dilate(C, If[3 < i ≤ 4, 4 - i, 0], B) → D'_1
  27. Vector(C, D'_1) → u
  28. Translate(p', u) → p''
  29. Rotate(p'', If[4 < i ≤ 5, (((i - 4) * 180))°, 180°], B) → p'''
  30. Dilate(B, If[5 < i ≤ 6, 6 - i, 0], E) → B'
  31. Dilate(C, If[5 < i ≤ 6, 6 - i, 0], E) → D'_2
  32. Segment(B, B') → r
  33. Segment(C, D'_2) → d
  34. Polygon(A, D, C) → poly2, d_2, a_2, e_1
  35. Polygon(D, B, C) → poly3, d_3, e_2, b_2
  36. Dilate(D, If[7 < i, 8 - i, 0], B) → E'
  37. Dilate(C, If[7 < i, 8 - i, 0], E) → D'_3
  38. Polygon(A, E', D'_3) → poly4, d'_3, a_3, e'
  39. Dilate(B, If[6 < i ≤ 7, 7 - i, 0], E) → B'_1
  40. Vector(B, B'_1) → v
  41. Translate(p''', v) → t
  42. Line(E, a) → c_3
  43. Circle(E, 1) → f_1
  44. Intersect(f_1, c_3, 2) → I
  45. Intersect(f_1, r, 1) → J
  46. Angle(I, E, J) → γ
  47. Rotate(t, If[7 < i ≤ 8, ((i - 7) * γ), γ], E) → t'
  48. Segment(A, B) → e