Question

use the figure and the given information to determine which lines, if any, are parallel. choose the correct justification, if necessary
given: ∠9 ≅ ∠11

• a∥b

if corresponding angles are congruent, then lines are parallel.
if alternate exterior angles are congruent, then lines are parallel.
○ p∥
if consecutive interior angles are supplementary, then lines are parallel.
if alternate interior angles are congruent, then lines are parallel.

Explanation:

Step1: Identify Angle Relationship

$\angle 9$ and $\angle 11$ are corresponding angles formed by transversal $q$ intersecting lines $a$ and $b$.

Step2: Apply Parallel Line Theorem

The theorem states: If corresponding angles are congruent, then lines are parallel. Since $\angle 9 \cong \angle 11$, by this theorem, lines $a$ and $b$ (denoted as $a \parallel b$) are parallel.

Answer:

$a \parallel b$ (because corresponding angles $\angle 9$ and $\angle 11$ are congruent, so by the corresponding angles congruent implies parallel lines theorem, $a$ and $b$ are parallel)