Question

given $\angle 4 \cong \angle 14$, which lines, if any, must be parallel based on the given information?
justify your conclusion

$a \parallel b$, converse of the same - side interior angles theorem
$a \parallel b$, converse of the alternate interior angles theorem
$a \parallel b$, converse of the corresponding angles theorem
not enough information to make a conclusion

Explanation:

To determine if lines are parallel using angle - congruence, we need to identify the relationship between the angles (like corresponding, alternate interior, same - side interior) and the transversal and the lines we are testing. $\angle4$ and $\angle14$: we first need to find the transversal and the two lines cut by the transversal. $\angle4$ is formed by lines $b$ and $d$, and $\angle14$ is formed by lines $a$ and $d$. There is no clear transversal that cuts lines $a$ and $b$ to create these angles in a way that we can apply the converse of parallel - line angle theorems (corresponding, alternate interior, same - side interior). So, we don't have enough information to conclude that any lines are parallel.

Answer:

not enough information to make a conclusion