The figure shows a triangle ABC with the
altitudes AA1, BB1, and CC1. If A2,
B2, and C2 are the orthocenters of triangles AB1C1, BA1C1,
and CA1B1, respectively, prove that the triangles A1B1C1
and A2B2C2 are congruent.
Note: The triangle A1B1C1
is called the orthic triangle of the triangle ABC.