# Proportional segments between parallelogram and triangle

In the figure, ABCD is a parallelogram, $F$ is in the prolongation of $AD$. If $EF=32$, $GF=24$ and $AD=DF$, $BE=?$

My try: I tried to do some proportions between the triangles $FDG$ and $BCG$ but got nothing. I'm 100% sure that this problem is about propotionality. Any hints?

• What Kind of triangle is $$\Delta ABC$$? – Dr. Sonnhard Graubner Apr 7 '18 at 18:20
• the problem doesn't say anything about that triangle. We don't know – Rodrigo Pizarro Apr 7 '18 at 18:26

By intercept theorem, $BG=GF=24$
$BE=BG+GF-EF=24+24-32=16$
• wouldn't be $BE=16$? – Rodrigo Pizarro Apr 7 '18 at 18:36