Question

$\angle 15 \cong \angle 13$
a) $w \parallel x$; alternate interior angles converse
b) $w \parallel x$; converse of corresponding angles thm.
c) $y \parallel z$; alternate exterior angles converse
d) $y \parallel z$; converse of corresponding angles thm

Explanation:

Step1: Identify Angle Relationship

$\angle 15$ and $\angle 13$ are alternate interior angles formed by transversal $y$ (or $z$? Wait, transversal is the slant line, and the two lines are $w$ (the leftmost vertical) and $x$ (the vertical with $x$ arrow). Wait, no, $\angle 15$ is between $w$ (left vertical) and the transversal, $\angle 13$ is between $x$ (right vertical with $x$ arrow) and the same transversal. So they are alternate interior angles.

Step2: Apply Converse Theorem

The Alternate Interior Angles Converse states that if alternate interior angles are congruent, then the two lines cut by the transversal are parallel. So since $\angle 15 \cong \angle 13$, lines $w$ and $x$ are parallel by Alternate Interior Angles Converse. So option A matches.

Answer:

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