Question

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

1. ∠1 ≅ ∠6
2. m∠7 + m∠6 = 180°

Explanation:

Step1: Analyze $\angle1\cong\angle6$

$\angle1$ and $\angle6$ are alternate exterior angles. If alternate exterior angles are congruent, then the lines are parallel.
Since $\angle1\cong\angle6$, by the Alternate Exterior Angles Theorem, $g\parallel h$.

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

$\angle7$ and $\angle6$ are same - side interior angles. If same - side interior angles are supplementary, then the lines are parallel.
Since $m\angle7 + m\angle6 = 180^{\circ}$, by the Same - Side Interior Angles Theorem, $g\parallel j$.

Answer:

1. $g\parallel h$ by the Alternate Exterior Angles Theorem.
2. $g\parallel j$ by the Same - Side Interior Angles Theorem.