Let $\Delta ABC$ and $\Delta EFD$ be triangles with sides $a$, $b$, $c$ and $d$, $e$, $f$. All sides have different lengths.
I am looking for a functional condition for sides when triangles can have the same heights $h_E=h_B$.
I have found the three cases when two triangles can have the same hights.
Case 1. Acute triangles