How about a couple of hints on this proof:
1. If you want to prove two angles congruent, then one way to attack that is to find two triangles, prove that they're congruent, and then match up the corresponding parts. So, for angles B and D, which two triangles might help you here?
2. What's the definition of a parallelogram, and what do you know about them? For example, you know stuff about their sides.
3. What are the different ways of proving two triangles congruent, to help you prove #1?
4. Can you figure out which properties of the parallelogram will help you with #3, once you decide on a way to prove the triangles congruent?
Hope this helps, and I'm sure more hints are on the way if you're still stuck.