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: \\( j \\| k \\) converse: alternate exterior angles

Explanation:

When two lines are cut by a transversal, if alternate exterior angles are congruent, then the two lines are parallel. Here, ∠12 and ∠15 are alternate exterior angles formed by lines \(j\) and \(k\) with transversal \(m\). Since \(∠12\cong∠15\), by the converse of the alternate - exterior angles theorem, lines \(j\) and \(k\) are parallel.

Answer:

Parallel Lines: \(j\parallel k\)
Converse: alternate exterior angles