Question

43 fill in the blank 4 points given \\( \angle 12 \cong \angle 15 \\), determine which lines, if any, are parallel. state the converse that justifies your answer. parallel lines: \\( 1 \\| \mathrm{m} \\) converse: alternate interior angles

Explanation:

Step1: Identify the relationship between the angles

$\angle12$ and $\angle15$ are alternate interior angles formed by lines $l$ and $m$ with transversal $n$.

Step2: Apply the converse of the alternate interior angles theorem

The converse of the alternate interior angles theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel. Since $\angle12\cong\angle15$, by the converse of the alternate interior angles theorem, $l\parallel m$.

Answer:

Parallel Lines: $l\parallel m$; Converse: converse of the alternate interior angles theorem.