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Angle Bisector Theorem Investigation

Angle Bisector Theorem Investigation
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2015-08-07 20:15
AngleTrigonometryGeometric Construction
This applet visually demonstrates the Angle Bisector Theorem by allowing students to investigate that if a point is equidistant from the sides of an angle, it lies on the angle bisector. Key concepts include angle bisectors, distances, and equidistant points. It is constructed using GeoGebra commands like Ray, Segment, OrthogonalLine, Circle, Intersect, and Angle. Suitable for middle school and high school students to explore geometric properties and proofs.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Ray(A, C) → b
  3. Segment(K, J) → c
  4. OrthogonalLine(A, a) → d
  5. Circle(A, c) → e
  6. Intersect(e, d) → F_1, G_1
  7. OrthogonalLine(F_1, d) → f
  8. OrthogonalLine(A, b) → g
  9. Circle(A, c) → h
  10. Intersect(h, g) → H_1, I_1
  11. OrthogonalLine(I_1, g) → i
  12. Intersect(f, i) → D
  13. OrthogonalLine(D, b) → j
  14. OrthogonalLine(D, a) → k
  15. Intersect(k, a) → E
  16. Intersect(j, b) → F
  17. Segment(D, E) → l
  18. Segment(D, F) → m
  19. Angle(C, F, D) → α
  20. Angle(D, F, A) → β
  21. Angle(A, E, D) → γ
  22. Angle(C, A, D) → δ
  23. Angle(D, A, B) → ε
  24. Ray(A, D) → n

AI Drawing Prompt Reference

Draw a triangle ABC with point D on the angle bisector of angle BAC. Construct perpendiculars from D to AB and AC, intersecting at points E and F respectively. Connect DE and DF, and measure the angles CDE, EDF, ADE, and CAD to explore the Angle Bisector Theorem.
The prompt above was compiled from the original drawing commands and is for reference only.