The figure shows a triangle ABC with the
altitudes AA_{1}, BB_{1}, and CC_{1}. If A_{2},
B_{2}, and C_{2} are the orthocenters of triangles AB_{1}C_{1}, BA_{1}C_{1},
and CA_{1}B_{1}, respectively, prove that the triangles A_{1}B_{1}C_{1}
and A_{2}B_{2}C_{2} are congruent.
Note: The triangle A_{1}B_{1}C_{1 }
is called the orthic triangle of the triangle ABC.
