Question

problem 13: from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ∠2≅∠3 prove: bc || ad

Explanation:

$\angle2$ and $\angle3$ are alternate - interior angles formed by lines $\overline{BC}$ and $\overline{AD}$ with transversal $\overline{AC}$. Since $\angle2\cong\angle3$, by the converse of the alternate - interior angles theorem (if alternate - interior angles are congruent, then the two lines are parallel), we can conclude that $\overline{BC}\parallel\overline{AD}$.

Answer:

If alternate - interior angles are congruent, then the lines are parallel.