Prove lines being parallel within a traiangle

Question

Here is the problem: The only condition given is $DF//BC$, is it possible to prove that $GH//BC$? Please verify it. Any help will be appreciated.

Answer 1

Yes ! $GH||BC$ Now since $G$ is midpoint of $DE$ and $H$ is midpoint of $EF$.

${\bf Claim}: \bigtriangleup DEF ~\& \bigtriangleup GEH$ are similar

Since $\frac{DE}{GE}=\frac{FE}{HE}$

and $\angle DEF=\angle GEH$.

and therefore from Side-Side-angle similarity theorem both the triangles are similar and hence $GH||BC$.