A triangle has vertices of P, Q , R

First, you start with writing out the triangle and the givens.

Angle Q = Angle Q -> Angles equal themselves

QM congruent QP -> QM is half of QP since M is the midpoint, so they're congruent

QN congruent QR -> Same reason as one above

Triangle QMN congruent Triangle QPR -> SAS

MN || PR -> Same Side Rule (Forgot what it's called exactly)

There ya have it

Those are some pretty diagrams, CoopTheDupe!

I am fairly certain that you were referring to the Triangle Proportionality Theorem when you stated "MN || PR -> Same Side Rule (Forgot what it's called exactly)"