which of the following theorems proves that abc~def?

Answer:
D but read below.
Step-by-step explanation:
I take it that the symbol ~ stands for similar. If that is so, then the answer you want is AA, because if 2 angles in a triangle are equal, then all 3 are. So if any 2 equal angles in one triangle are equal to 2 angles in another, then the two triangles are similar.