Question

if ∠9 ≅ ∠15, which lines, if any, are parallel? state the postulate or theorem that justifies your answer.
text alternative
diagram of lines a, b, l, m with angles numbered 1 - 16
a) a || b; converse of the corresponding angles theorem
b) ℓ || m; alternate exterior angles converse
c) a || b; alternate exterior angles converse
d) it is not possible to determine whether any lines are parallel.

Explanation:

We know that $\angle9\cong\angle15$. To determine parallel lines, we analyze the angles:

• $\angle9$ and $\angle15$ are alternate exterior angles.
• The Alternate Exterior Angles Converse states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.
• Here, the transversal is the line intersecting $l$ and $m$, and $\angle9$ (on line $l$) and $\angle15$ (on line $m$) are alternate exterior angles. So by the Alternate Exterior Angles Converse, $l\parallel m$.

Answer:

B) $l \parallel m$; Alternate Exterior Angles Converse