The completion of the proof that QT/PR=ST/RS shows us that:
Reason 3: AA Similarity
Similar Triangles?
Two triangles are said to be similar if the ratio of their corresponding sides are equal.
The two column proof here is as follows:
Statement 1: ∠P ≅ ∠Q
Reason 1: Given
Statement 2: ∠PSR ≅ ∠PST
Reason 2: Vertical Angle Theorem
Statement 3: QT/PR = ST/RS
Reason 3: AA Similarity