The proof is 100% correct. Nice work.
The first statement simply repeats everything that is given.
The second statement uses the alternate interior theorem to say that angles 1 and 2 are congruent
Angles 2 and 3 are congruent after we connect the first two statements together with the transitive property.
Then directly from statement 3, we can use the alternate exterior angle converse to prove what your teacher wants.
