Hello!

I can't seem to solve through this problem. I have a triangle (pic attached). I need to show EF is parallel to BC given BD=DC, and angle EDB = angle ADE, and angle ADF = angle FDC. How do I do it? I really tried for a while, and here are some of my observations:

Angle EDF is a right angle since 2*alpha+2*beta = 180, therefore alpha+beta = 90. And I'm trying to show equality of alternate angles but with no success.

THANK YOU!!!!!!!!!!!!!!!!!!