Given: △ABC≅△DEF, △KLM≅△DEF
Prove: △ABC≅△KLM

Set up as a two-column proof.
There are three triangles they are equal to each other.

Triangle 1: ∠A, ∠B, ∠C
Triangle 2: ∠D, ∠E, ∠F
Triangle 3: ∠K, ∠L, ∠M