Help with this problem?

[afoster]

I had this problem on a test yesterday.

How would I solve this?
P.S. The unit was based around finding congruent triangles, so I'm fairly certain the goal is to find that the triangles are congruent in order to prove that the two angles are congruent. I think there is a way to prove the angles congruent without having to prove the triangles congruent, though.

 

[stapel]

I had this problem on a test yesterday.

How would I solve this?
P.S. The unit was based around finding congruent triangles, so I'm fairly certain the goal is to find that the triangles are congruent in order to prove that the two angles are congruent. I think there is a way to prove the angles congruent without having to prove the triangles congruent, though.

Are we to assume, contrary to the graphic, that E lies on BC? Or are we to extend AE until it meets BC at, say, F? Does the first "given" mean that the lengths of AB and AD are the same?

What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!