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