It isn't clear what the elements of your flowchart are supposed to look like. In general, the proof would go like this:
1. List the "givens": PQ=6=TS; ∠P=120°=∠T; ∠PRQ and ∠TRS are vertical angles.
2. Note that the vertical angles are congruent
3. Claim ΔPRQ ≅ ΔTRS by the AAS congruence postulate since two corresponding adjacent angles and the corresponding sides not between them have been shown to be congruent.
