In the figure,$x=y$ and $a=b$. Prove that $l \parallel n$.

(N/A) Given: $x=y$ and $a=b$.
$1$. For lines $l$ and $m$ with a transversal,the corresponding angles $x$ and $y$ are equal $(x=y)$. By the converse of the corresponding angles axiom,if corresponding angles are equal,then the lines are parallel. Therefore,$l \parallel m$ $....(1)$
$2$. For lines $n$ and $m$ with a transversal,the corresponding angles $a$ and $b$ are equal $(a=b)$. By the converse of the corresponding angles axiom,if corresponding angles are equal,then the lines are parallel. Therefore,$n \parallel m$ $....(2)$
$3$. From $(1)$ and $(2)$,since both lines $l$ and $n$ are parallel to the same line $m$,it follows that $l \parallel n$ (Lines parallel to the same line are parallel to each other).