Question

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

(lparallel m), by the converse of the same - side interior angles postulate

(lparallel m), by the converse of the alternate interior angles theorem

(rparallel s), by the converse of the same - side interior angles postulate

(rparallel s), by the converse of the alternate interior angles theorem

Explanation:

Step1: Identify angle - type

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

Step2: Apply angle - line relationship

The Converse of the Alternate Interior Angles Theorem states that if two 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