Answer:
[tex]\overline{vw} \cong \overline{rw}[/tex]
Step-by-step explanation:
AAS tells us that two traingles are coungruent if two angles are congruent and their corresponding opposite sides are congruent. From the picture we know that the segments [tex]\overline{xv}[/tex] and [tex]\line{RT}[/tex] are parallel, hence [tex]\angle X \cong \angle T[/tex] and [tex]\angle V \cong \angle R[/tex]. Moreover, since the two angles [tex]\angle VWX[/tex] and [tex]\RWT[/tex] are opposite by a vertex, they are also congruent.
On the other hand, the picture tells us that [tex]\overline{wx}\cong\overline{wt}[/tex]. Therefore, since we already know that [tex]\angle VWX \cong \angle RWT[/tex] and that [tex]\angle R \cong \angle V[/tex], we are only missing the information that [tex]\overline{vw} \cong \overline{rw}[/tex] to know that [tex]\triangle XWV \cong \triangle RWT[/tex] by AAS.
