Question

given the following information, determine which lines, if any, are parallel. state the theorem that justifies your answer.

1. \\( \angle 7 \cong \angle 6 \\)
2. \\( m \angle 7 + m \angle 6 = 180 ^ { \circ } \\)

Explanation:

Step1: Analyze ∠7 ≅ ∠6

∠7 and ∠6 are alternate interior angles. If alternate interior angles are congruent, then the lines are parallel.
So, by the Alternate Interior Angles Theorem, \(l\parallel m\).

Step2: Analyze \(m\angle7 + m\angle6=180^{\circ}\)

∠7 and ∠6 are same - side interior angles. If same - side interior angles are supplementary, then the lines are parallel.
So, by the Same - Side Interior Angles Theorem, \(l\parallel m\).

Answer:

For \(∠7 ≅ ∠6\), \(l\parallel m\) by the Alternate Interior Angles Theorem. For \(m\angle7 + m\angle6 = 180^{\circ}\), \(l\parallel m\) by the Same - Side Interior Angles Theorem.