Help with proof of parallel line?

You should be able to see a SAS similarity comparison between triange AMN and ABC

2*AN = AC AND 2*AM = AB

They also share angle A

So these triangles are similar.

Then m<ANM = m<ACB

You should have some things you can use to show then when lines {here MN and BC}

crossed by a transversal {AC}

if corresponding angles are congruent, then the lines crossed by the transversal must be parallel.

Probably Converse of AIA, but can't remember for sure. I always get AIA and CAIA crossed.