Prove the ratio of distances $d(P_1,P_2):d(P_2,P_3)$ is independant of line M

Question

If $L_1,L_2,L_3$ are three parallel lines in $\Bbb E^2$, and they meet in a line M in $P_1,P_2,P_3$.then the (signed) ratio of distances $d(P_1,P_2):d(P_2,P_3)$ is independent of M.

I can see that this is true, but I don't know how I could prove this in a correct way.

I'd appreciate some hints, about what kind of prove I need, or some other theorems I need to prove this one.

Answer 1

Hint

The triangles formed by $M$ on $L_1,L_2,L_3$ are similar.