Question

problem 15: (first taught in lesson 26) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ∠1 ≅ ∠3 prove: ad || bc

Explanation:

Step1: Identify angle relationship

$\angle1$ and $\angle3$ are alternate - interior angles formed by lines $\overline{AD}$ and $\overline{BC}$ with transversal $\overline{BD}$.

Step2: Apply parallel - line theorem

Since $\angle1\cong\angle3$ (given), by the theorem that if two lines are cut by a transversal and the alternate - interior angles are congruent, then the lines are parallel, we can conclude that $\overline{AD}\parallel\overline{BC}$.

Answer:

If two lines are cut by a transversal and the alternate - interior angles are congruent, then the lines are parallel.