The prove, triangle PTS is congruent to triangle RTQ. is achieved using SAS congruence theorem
How to complete the proof
The two column proof is written as follows
Statement Reason
T midpoint of PR and SQ given
PT ≅ TR Definition of midpoint
ST ≅ TQ Definition of midpoint
∠ PTS ≅ ∠ RTQ Vertical angle theorem
Δ PTS ≅ Δ RTQ SAS congruence theorem