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Converse of the Angle Bisector Theorem

Converse of the Angle Bisector Theorem
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2015-11-26 06:53
TriangleAngleGeometric Construction
This example demonstrates the application of the Converse of the Angle Bisector Theorem in triangles, showing that if a point inside a triangle is equidistant from two sides, it lies on the angle bisector. Core mathematical concepts include angle bisectors, distances, and geometric constructions. It uses commands like Segment, Angle, AngularBisector, Point, Distance, OrthogonalLine, and Intersect in GeoGebra. Suitable for high school students learning about the inverse theorem and its applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Angle(A, B, C) → β
  4. AngularBisector(A, B, C) → c
  5. Point(c) → D
  6. Point(a) → E
  7. Point(b) → F
  8. Distance(E, D) → distanceED
  9. OrthogonalLine(D, a) → d
  10. Intersect(a, d) → G
  11. Intersect(d, a) → H
  12. Intersect(c, d) → I
  13. Segment(D, G) → e
  14. Angle(E, G, D) → α
  15. OrthogonalLine(D, b) → f
  16. Intersect(b, f) → J
  17. Segment(D, J) → g
  18. Angle(D, J, B) → γ
  19. Angle(c, b) → δ
  20. Distance(g, e) → h
  21. Angle(D, B, J) → ε
  22. Angle(G, B, D) → ζ
  23. Point(a) → K
  24. Point(b) → L
  25. Segment(K, M) → i
  26. Segment(M, L) → j
  27. Distance(j, i) → k
  28. Angle(B, K, M) → η
  29. Angle(M, L, B) → θ
  30. Angle(D, H, B) → ι
  31. Angle(D, J, B) → κ