QR || ST & QT=RS
That could be an isosceles trapezoid. Don't check this one.
QR=ST & QR || ST
Congruent Parallel sides. CHECK ME.
QT || RS & QR=ST.
Basically the same as the first, don't check.
QR=ST & QT=RS
Quadrilateral with equal opposite sides is a parallelogram. CHECK ME
QR=ST & ST=ST
ST=ST is not news. Congruent opposite sides. Don't check me.