Question

which lines are parallel if (mangle3 = mangle6)? justify your answer.

1. (rparallel s), by the converse of the alternate interior angles theorem
2. (rparallel s), by the converse of the same - side interior angles postulate
3. (lparallel m), by the converse of the alternate interior angles theorem
4. (lparallel m), by the converse of the same - side interior angles postulate

Explanation:

Step1: Identify angle - type relationship

$\angle3$ and $\angle6$ are alternate interior angles formed by lines $r$ and $s$ and transversal $l$.

Step2: Apply the converse of the alternate - interior angles theorem

The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel. Since $m\angle3 = m\angle6$, lines $r$ and $s$ are parallel.

Answer:

$r\parallel s$, by the Converse of the Alternate Interior Angles Theorem