Question

from each given statement below, select the definition, property, postulate, or theorem that justifies each prove statement.
(b)10. given: ∠l≅∠m
(a) prove: pl∥mn
a. if two lines form congruent corresponding angles with a transversal, then the lines are parallel.
b. definition of congruent angles
c. if two lines form congruent alternate interior angles with a transversal, then the lines are parallel.
d. if two parallel lines are cut by a transversal, then their alternate interior angles are congruent.
if two lines form congruent alternate exterior angles with a transversal, then the lines are parallel.

Explanation:

Step1: Identify angle - type relationship

We are given that $\angle L\cong\angle M$. These are alternate interior angles formed by lines $\overline{PL}$ and $\overline{MN}$ with a transversal (the line passing through $L$ and $M$).

Step2: Apply parallel - line theorem

The theorem that states if two lines form congruent alternate interior angles with a transversal, then the lines are parallel is used to prove $\overline{PL}\parallel\overline{MN}$.

Answer:

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