Assume that line $r$ $\parallel$ line $s$. Them $\angle$1 $\cong$ $\angle$ 5 because they are corresponding angles. But it is given that $\angle$1 $\ncong$ $\angle$5, which leads to a contradiction. Thus, the assumption that that $r$ $\parallel$ $s$ is false and it follows that $r$ $\nparallel$ $s$.
Work Step by Step
Work cannot be shown for a proof. Logic is the only work done in such instances.