Here it can be appropriate to separate the two triangles. However, let's first recognize that they share WV as a side. Therefore, in addition to the given information, we can by the Reflexive Property of Congruence say that WV in the two triangles are congruent.
Having separated the triangles, we notice that WZ consists of two smaller segments, WY and YZ. We also see that V'X consists of the two smaller segments V'Y' and Y'X. By the Segment Addition Postulate we can write the following equation
&WZ=WY+YZ
&VX=V'Y'+Y'X
Since WY≅V'Y' and YZ≅ Y'X, we can use the Substitution Property of Equality to rewrite one of these equations.
&WZ= V'Y'+ Y'X
&VX=V'Y'+Y'X
Finally, we have enough information to prove the triangle's third side are congruent as well by using the Transitive Property of Congruence.
&WZ= V'Y'+ Y'X
&VX= V'Y'+ Y'X
&VX=WZ
Now that we know all corresponding sides are congruent, we can by the SSS Congruence Theorem claim that △ VWX ≅ △ WVZ. Let's write this as a two-column proof as well. Note that we wont assume that we separate the triangles when we write the two-column proof.
