Question

practice
for exercises 12 - 15, use the given information.
which lines in the figure can you conclude are
parallel? state the theorem that justifies each
answer. see examples 1 and 3

1. \\( \angle 2 \cong \angle 3 \\) 13. \\( \angle 6 \cong \angle 7 \\)
2. \\( \angle 1 \cong \angle 4 \\) 15. \\( m \angle 5 + m \angle 8 = 180 ^ { \circ } \\)

Explanation:

Step1: Analyze ∠2 and ∠3

∠2 and ∠3 are alternate interior angles. If alternate interior angles are congruent, then the lines are parallel.

Step2: Identify the lines

The lines cut by the transversal such that ∠2 and ∠3 are alternate - interior angles are \(r\) and \(p\).

Answer:

Lines \(r\) and \(p\) are parallel. The theorem is the Alternate Interior Angles Theorem.