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Cameron wants to prove the Alternate Interior Angles Theorem. In the diagram, $\overleftrightarrow{P Q} \| \overleftrightarrow{R S}$$\newline$Complete Cameron's proof that alternate interior angles $\angle P V W$ and $\angle V W S$ are congruent.$\newline$Construct the midpoint $M$ of $\overline{W V}$, then rotate $\overleftrightarrow{P Q}, \overleftrightarrow{R S}$, and $\overleftrightarrow{T U} 180^{\circ}$ about $M$ to get $\overleftrightarrow{P^{\prime} Q^{\prime}}, \overleftrightarrow{R^{\prime} S^{\prime}}$, and $\overleftrightarrow{T^{\prime} U^{\prime}}$. Since $M$ lies on $\angle P V W$$1$ and the rotation is $\angle P V W$$2$ coincides with $\angle P V W$$3$ are equidistant from $M$ on $\angle P V W$$1$, so $\angle P V W$$6$ coincides with $\angle P V W$$7$ and $\angle P V W$$8$ coincides with $\angle P V W$$3$$\newline$A $\angle V W S$$0$ rotation of a line is a parallel line, and the only line parallel to $\angle V W S$$1$ that passes through $\angle P V W$$7$ is $\angle P V W$$3$ Therefore, $\angle P V W$$3$ coincide, and $\angle V W S$$5$ and $\angle V W S$$6$ coincide. So, the rotation maps $\angle P V W$$3$$\newline$Since rotation $\angle P V W$$3$ , $\angle V W S$$9$.