orthocentre and triangle related question

Question

$AD$, $BE$, and $CF$ are the altitudes of triangle $ABC$ with orthocentre $H$, then $C$ is the orthocentre of which triangle?

Answer: triangle $ABH$.

Please explain.

Answer 1

These diagrams should make it clear. In each diagram, the brown thick segments are the relevant triangle, with shaded interior. The black segments are altitudes, and the dashed segments are extensions of the sides or the altitudes. The points and line segments are exactly the same in both diagrams: only the interpretation changes, along with the triangle being considered.

In the first diagram, we see that point $H$ is the intersection of the altitudes of triangle $ABC$.

In the second diagram, we see that point $C$ is the intersection of the (extended) altitudes of triangle $ABH$.

Is it clear now?