I've got exercise to do as en exercise to my school leaving exam and I have no idea how to prove it:
Diagonals of trapezium intersect in point $S$. Through point $S$ the segment was given that is parallel to the bases and intersect the legs in points $E$ and $F$. Prove that $|ES| = |SF|$.
I'm sorry for my poor translation but I'm not good at math english yet.