If we can show that △ WQV ≅ △ TVR, then we know that QW ≅ VT. Let's start by separating the triangles.
Since we know two angles and a non-included side, we can by the AAS Congruence Theorem prove that △ WQV ≅ △ TVR. Now we know that QW ≅ VT since these are corresponding sides.