Question

use the diagram and the given information to determine if m || n, p || q, or neither. given: ∠10 ≅ ∠14
m || n
p || q
neither

Explanation:

Step1: Recall parallel - line theorem

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. $\angle10$ and $\angle14$ are alternate interior angles formed by lines $p$ and $q$ with a transversal.

Step2: Apply the theorem

Since $\angle10\cong\angle14$, by the alternate - interior angles converse, $p\parallel q$.

Answer:

$p\parallel q$