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Triangle Angle Bisector, Incenter, and Triangle Inequality

Triangle Angle Bisector, Incenter, and Triangle Inequality
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2019-01-02 10:04
TriangleAngleGeometric Construction
In collections Parts of a Triangle
This example demonstrates the angle bisector, incenter, and triangle inequality. Key mathematical concepts include angle bisector, incenter, and triangle inequality. It is constructed using GeoGebra commands such as Polygon, AngularBisector, Intersect, etc. Suitable for middle school and above students to learn geometric construction and related theorems.

GeoGebra Commands & Parameters

  1. Polygon(C, B, D) → t5, c_1, a_1, b_1
  2. AngularBisector(D, C, B) → m
  3. AngularBisector(D, B, C) → n
  4. AngularBisector(B, D, C) → p
  5. Intersect(m, n) → H
  6. Intersect(m, a_1) → E_1
  7. Intersect(n, b_1) → F_1
  8. Intersect(p, c_1) → G_1
  9. Segment(B, F_1) → q
  10. Segment(D, G_1) → r
  11. Segment(C, E_1) → s
  12. Distance(H, E_1) → distanceD1E1
  13. Distance(H, F_1) → distanceD1F1
  14. Distance(H, G_1) → distanceD1G1
  15. Segment(B, H) → l_1
  16. Segment(C, H) → d_1
  17. Segment(D, H) → e_1
  18. OrthogonalLine(H, a_1) → f_2
  19. Intersect(f_2, a_1) → E
  20. OrthogonalLine(H, b_1) → h_2
  21. Intersect(h_2, b_1) → G
  22. Segment(G, H) → HG
  23. OrthogonalLine(H, c_1) → j_2
  24. Intersect(j_2, c_1) → F
  25. Segment(F, H) → HF
  26. Polygon(I, J, K) → t1, k, i, j
  27. AngularBisector(K, J, I) → f
  28. Intersect(f, j) → L
  29. Segment(J, L) → g
  30. Angle(L, J, K) → γ
  31. Angle(I, J, L) → δ
  32. Angle(F, B, H) → ε
  33. Angle(H, B, E) → ζ
  34. Angle(H, C, F) → η
  35. Angle(G, C, H) → θ
  36. Angle(E, D, H) → ι
  37. Angle(H, D, G) → κ
  38. Segment(H, E) → HE
  39. Circle(O, 4) → c
  40. Point(c) → P
  41. Segment(O, P) → h
  42. Circle(P, 6) → d
  43. Point(d) → Q
  44. Segment(P, Q) → l
  45. Segment(O, Q) → t
  46. Circle(H, E) → e