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Explore Isogonal Conjugate Points

Explore Isogonal Conjugate Points
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2015-02-15 20:37
TriangleAngleTransformation
In collections A Tour of Triangle Geometry
This example demonstrates isogonal conjugate points for different lines intersecting the Euler line. By dragging point X or the triangle vertices, observe the changes in isogonal conjugate points. Key mathematical concepts include triangles, lines, mirrors, midpoints, etc. GeoGebra commands used include Circle, Line, OrthogonalLine, Intersect, Mirror, Midpoint, etc. Suitable for high school geometry learning.

GeoGebra Commands & Parameters

  1. Circle(A, B, C) → d
  2. Center(d) → O
  3. Line(A, B) → a
  4. Line(B, C) → b
  5. Line(C, A) → c
  6. OrthogonalLine(C, a) → e
  7. OrthogonalLine(A, b) → f
  8. Intersect(e, f) → H
  9. Mirror(H, O) → L
  10. Midpoint(B, A) → D
  11. Segment(C, D) → h
  12. Midpoint(B, C) → E
  13. Midpoint(C, A) → F
  14. Circle(D, F, E) → k
  15. Center(k) → N
  16. Line(H, O) → g
  17. Line(H, L) → i
  18. Point(g) → X
  19. Circle(X, 2) → p
  20. Point(p) → I
  21. Line(X, I) → j
  22. Point(j) → J
  23. Mirror(J, c) → J'
  24. Mirror(J, a) → J'_1
  25. Mirror(J, b) → J'_2
  26. Circle(J'_1, J', J'_2) → q
  27. Center(q) → K
  28. Locus(K, J) → loc1
  29. Polygon(A, B, C) → poly1, c_1, a_1, b_1