\(\overline{SV}||\overline{TU}\) (this is given in the first sentence)
3. \(\angle XSV\cong\angle XUT\) and \(\angle XVS\cong\angle XTU\) due to ...
7. ... the alternate interior angles theorem (which holds because \(\overline{ST}\) and \(\overline{TU}\) are parallel)
8. Because the above establishes that \(\Delta SXT\cong\Delta UXV\), which means \(\overline{ST}||\overline{UV}\), which in turn means \(VUTS\) is a parallelogram.
