Proportionality and Thales Theorem let $k$ and $l$ be parallel lines. Let $A, B, C$ be points on $k$ and $A' B', C'$ be points on $l$ such that the lines $AA', BB'$ and $CC'$ intersect at a common point. Prove that $\frac{|A'B'|}{|B'C'|}=\frac{|AB|}{|BC|}$.
I tried using Thales's theorem on proportionality but I got confused
Any hints,
Thanks

If $O$ is the common point of $AA'$, $BB'$ and $CC'$, notice that triangle $ABO$ is similar to $A'B'O$ and triangle $BCO$ is similar to $B'C'O$. From that the assertion follows.
