Question

t is the midpoint of pr and qs. complete the proof that △pst ≅ △rqt.
1 t is the midpoint of pr given
2 t is the midpoint of qs given
3 qr ≅ ps given
4 pt ≅ rt definition of midpoint
5

Explanation:

Step1: Identify vertical angles

$\angle STP\cong\angle R T Q$ (Vertical angles are congruent)

Step2: Use mid - point property for another segment

Since \(I\) is the midpoint of \(QS\), \(ST = QT\) (Definition of mid - point)

Step3: Apply SAS (Side - Angle - Side) congruence criterion

In \(\triangle PST\) and \(\triangle RQT\), we have \(PS = QR\) (Given), \(\angle STP=\angle RTQ\) (Vertical angles), \(ST = QT\) (From mid - point of \(QS\)). So, \(\triangle PST\cong\triangle RQT\) (SAS congruence criterion)

Answer:

\(\triangle PST\cong\triangle RQT\) (by SAS congruence criterion)