Question

given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.
14.
\\( \angle 4 \cong \angle 20 \\)

Explanation:

Step1: Analyze the relationship between angles

We know that if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Also, vertical angles are congruent by nature (\(\angle4\cong\angle8\) as vertical angles). Given \(\angle4\cong\angle20\), then \(\angle8\cong\angle20\) (by transitive property of congruence: if \(a = b\) and \(b = c\), then \(a=c\)).

Step2: Apply the converse of corresponding angles theorem

\(\angle8\) and \(\angle20\) are corresponding angles. The converse of the corresponding angles theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Here, lines \(l\) and \(n\) are cut by a transversal, and since \(\angle8\cong\angle20\), lines \(l\) and \(n\) are parallel.

Answer:

parallel lines: \(l\) and \(n\), converse: corresponding angles converse