Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ∠l ≅ ∠m prove: \\(\overline{pl} \parallel \overline{mn}\\) diagram of points p, l, m, n a b c d e if two lines form congruent corresponding angles with a transversal, then the lines are parallel.

Explanation:

We need to justify \( \overline{PL} \parallel \overline{MN} \) given \( \angle L\cong\angle M \). The transversal here is \( \overline{LM} \) (connecting \( L \) and \( M \)). \( \angle L \) and \( \angle M \) are corresponding angles formed by transversal \( \overline{LM} \) with lines \( \overline{PL} \) and \( \overline{MN} \). Since the angles are congruent, by the theorem in option A (if two lines form congruent corresponding angles with a transversal, the lines are parallel), we can conclude \( \overline{PL} \parallel \overline{MN} \).

Answer:

A. If two lines form congruent corresponding angles with a transversal, then the lines are parallel.