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Isogonal Line as Perpendicular Bisector of Reflection Triangle

Isogonal Line as Perpendicular Bisector of Reflection Triangle
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2015-02-16 09:22
TriangleGeometric Construction
In collections Reflections in Triangle Geometry
This example demonstrates the relationship between an isogonal line and the perpendicular bisector of a reflection triangle. Key math concepts include isogonal lines, reflection triangles, perpendicular bisectors, and geometric transformations. Construction involves commands like Polygon, Mirror, Segment, AngularBisector, Line, Intersect, and Point in GeoGebra. Suitable for high school mathematics education to understand properties of isogonal lines and reflection transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Mirror(P, b) → P'
  3. Mirror(P, c) → P'_1
  4. Mirror(P, a) → P'_2
  5. Segment(P'_1, P'_2) → d
  6. Segment(P'_2, P') → e
  7. Segment(P', P'_1) → f
  8. Segment(P, P') → g
  9. Segment(P'_1, P) → h
  10. Segment(P, P'_2) → i
  11. AngularBisector(B, A, C) → j
  12. AngularBisector(C, B, A) → k
  13. Line(A, P) → l
  14. Line(B, P) → m
  15. Mirror(l, j) → l'
  16. Mirror(m, k) → m'
  17. Intersect(l', m') → D
  18. Line(A, P) → n
  19. Mirror(n, j) → n'
  20. Point(n') → E
  21. Segment(E, P'_1) → p
  22. Segment(E, P') → q