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The orthocenters of the three triangles are located on the opposite vertex.

The orthocenters of the three triangles formed by the vertices of triangle ABC and its orthocenter are the same as the orthocenter of triangle ABC.

Let's examine triangle BHC. The orthocenter is found by constructing the line through point H which is perpendicular to BC, the line through point C which is perpendicular to BH, and the line through point B which is perpendicular to HC.

Since, by the definition of orthocenter, HC is perpendicular to BA and HB is perpendicular to AC, the point of intersection of these two lines (point A) forms the orthocenter of triangle BHC. This can be verified by the fact that point A lies on the line perpendicular to BC through H.

This holds true for all triangles formed by the orthocenter and two vertices of a triangle, because in the proof above, no measurements or qualifications specific to any special case were utilized.