Similar triangles
Since the lines LM and PQ are parallel, the angles
∠L and ∠Q are congruent
because they are alternate interior angles
∠M and ∠P are congruent
because they are alternate interior angles too.
And the angles
∠PNQ and ∠MNL are congruent too
because they are vertical angles
We have the congruent angles are:
Conclusion
Since both triangles have the same angles they ARE similar by AAA similarity .
Naming the triangles in the same angles order, we have that triangle
ΔLMN is similar to triangle ΔQPN