Question

given xy || zw
prove △xyv ~ △zwv
use the drop - down menus to complete the paragraph proof
we are given that \\( \overline { x y } \\) is parallel to \\( \overline { z w } \\). if \\( \overline { x z } \\) is a transversal that intercepts \\( \overline { x y } \\) and \\( \overline { z w } \\), angle yxv and angle are alternate interior angles. since \\( \overline { x y } \\) is p w, we know that these angles are congru also know that angle xvy and angle zvw tical angles, and thus congruent. x zvw include that \\( \triangle x y v \sim \triangle z w v \\) using the wzv arity theorem

Explanation:

Step1: Recall alternate - interior angles definition

When a transversal intersects two parallel lines, alternate - interior angles are non - adjacent interior angles on opposite sides of the transversal.

Step2: Identify the alternate - interior angle

Since \(XY\parallel ZW\) and \(XZ\) is the transversal, for \(\angle YXV\), the alternate - interior angle is \(\angle ZWV\) (because they are between the parallel lines \(XY\) and \(ZW\) and on opposite sides of the transversal \(XZ\)).

Answer:

\(\angle ZWV\)