These two trees are not equivalent

Question

Two trees $T_{1}$ and $T_{2}$ in the plane are equivalent if there exists a homeomorphism $f$ of the plane such that $f(T_{1})=T_{2}$. Suppose we are given the following two trees in the picture

I need to prove that they are not equivalent in the sense defined above. I am quite stuck here. Any insight would be helpful.

Answer 1

Hint: Let $l$ be the horizontal line segment in $T_1$ and consider the line $L$ containing $l$. How does it divide the plane?