Explanation:
QR is parallel to TU | Given 
 
S is the midpoint of QT | Given 
 
QS = ST | Definition of midpoint 
 
<QSR = <TSU | definition of vertical angles 
 
<QRS = <STU | Definition of Alternate Interior Angles 
 
QSR = TSU | ASA 
 
Pretty sure that's right :D 
 
Also, wherever it says "=", I mean congruency symbol