Question

∠15 ≅ ∠13
a) w || x; alternate interior angles converse
b) w || x; converse of corresponding angles thm.
c) y || z; alternate exterior angles converse
d) y || z; converse of corresponding angles thm.

Explanation:

Step1: Identify Angle Relationship

$\angle 15$ and $\angle 13$ are alternate interior angles formed by transversal (the slant line) intersecting lines $w$ and $x$.

Step2: Apply Converse Theorem

The Alternate Interior Angles Converse states that if alternate interior angles are congruent, then the lines are parallel. Since $\angle 15 \cong \angle 13$, lines $w$ and $x$ are parallel by this converse. So the correct option is A.

Answer:

A) $w \parallel x$; Alternate Interior Angles Converse