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Concurrency Theorem

Concurrency Theorem
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2015-11-02 10:13
TriangleAngleGeometric Construction
In collections Geometry|CH3: Constructions
This example demonstrates the concurrency theorem, involving angle bisectors and medians in a triangle. Using GeoGebra commands such as Polygon, LineBisector, and Intersect, one can construct concurrent lines. Suitable for middle school and above students to learn geometric construction and related theorems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(b) → d
  3. LineBisector(a) → e
  4. LineBisector(c) → f
  5. Intersect(d, e) → D
  6. AngularBisector(c, a) → g, h
  7. AngularBisector(a, b) → i, j
  8. AngularBisector(b, c) → k, l
  9. Intersect(h, j) → E
  10. Intersect(e, a) → F
  11. Intersect(f, c) → G
  12. Intersect(d, b) → H
  13. Segment(A, F) → m
  14. Segment(B, H) → n
  15. Segment(C, G) → p
  16. Intersect(m, n) → I
  17. OrthogonalLine(B, b) → q
  18. OrthogonalLine(C, c) → r
  19. OrthogonalLine(A, a) → s
  20. Intersect(q, r) → J
  21. Segment(D, J) → d_1
  22. Circle(D, B) → f_1
  23. OrthogonalLine(E, a) → h_1
  24. Intersect(h_1, a) → K
  25. Circle(E, K) → k_1

AI Drawing Prompt Reference

Draw a triangle ABC, then draw its three angle bisectors and medians to find their intersection points D, E, F, G, H. Next, draw the perpendicular bisectors of AB, BC, and CA to find their intersection point J. Finally, draw circles centered at D, E, and F, and another circle centered at E with a point K.
The prompt above was compiled from the original drawing commands and is for reference only.