Question

given pq is parallel to st and r is the mid - point of qt, complete the statement below. due to the given information, it can be concluded that △prq≅△srt by or by aas asa sss sas aaa hl

Explanation:

Step1: Identify equal - angle pairs

Since \(PQ\parallel ST\), alternate - interior angles are equal. So, \(\angle PQR=\angle STR\) and \(\angle QPR=\angle TSR\).

Step2: Identify equal - side pair

Given that \(R\) is the mid - point of \(QT\), then \(QR = TR\).

Step3: Determine congruence criterion

We have two pairs of equal angles and the included side between them is equal. By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle PRQ\cong\triangle SRT\). Also, with two pairs of angles and a non - included side equal, we can use the Angle - Angle - Side (AAS) congruence criterion.

Answer:

AAS, ASA