Question

problem 14. (lesson 23) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: $overline{mn}paralleloverline{lo}$ prove: $angle{omn}congangle{lom}$

Explanation:

Step1: Identify parallel lines

Given $\overline{MN}\parallel\overline{LO}$.

Step2: Identify the angle - pair

$\angle OMN$ and $\angle LOM$ are alternate - interior angles formed by the parallel lines $\overline{MN}$ and $\overline{LO}$ with the transversal $\overline{MO}$.

Step3: Apply the theorem

By the alternate - interior angles theorem, when two parallel lines are cut by a transversal, the alternate - interior angles are congruent. So, $\angle OMN\cong\angle LOM$.

Answer:

Theorem of alternate - interior angles.