Since the triangles ΔQRS and ΔTUV, their corresponding sides are also congruent, this means that
[tex]\begin{gathered} QR\cong TU \\ RS\cong UV \\ QS\cong TV \end{gathered}[/tex]Since QS and TV are congruent, this means that they have the same measures, therefore
[tex]\begin{gathered} QS=TV \\ 3v+2=7v-6 \end{gathered}[/tex]Solving this equation for v, we have
[tex]\begin{gathered} 3v+2=7v-6 \\ 3v-7v+2=-6 \\ -4v=-6-2 \\ 4v=8 \\ v=2 \end{gathered}[/tex]Using this value for v in our expression for the sides, we have
[tex]\begin{gathered} QS=3\cdot2+2=8 \\ TV=7\cdot2-6=8 \end{gathered}[/tex]Both sides are equal to 8.
