Question

given: \\(\overline{xy} \parallel \overline{zw}\\)\
prove: \\(\triangle xyv \sim \triangle zwv\\)\
use the drop-down menus to complete the paragraph proof.\
we are given that \\(\overline{xy}\\) is parallel to \\(\overline{zw}\\). if \\(\overline{xz}\\) is a transversal that intercepts \\(xy\\) and \\(zw\\), angle \\(\boldsymbol{\square}\\) and angle \\(\boldsymbol{\square}\\) are alternate interior angles. since \\(xy\\) is parallel to \\(zw\\), we know that these angles are \\(\boldsymbol{\square}\\). we also know that angle \\(xvy\\) and angle \\(zvwv\\) are \\(\boldsymbol{\square}\\) angles, and thus congruent. we can conclude that \\(\triangle xyv \sim \triangle zwv\\) using the \\(\boldsymbol{\square}\\) similarity theorem.

Explanation:

Step1: Identify alternate interior angles

Transversal $\overline{XZ}$ intersects $\overline{XY}$ and $\overline{ZW}$, so $\angle XVY$ and $\angle ZVW$ are not alternate interior angles here—correction: $\angle X$ and $\angle Z$ (alternate interior angles from transversal $\overline{XZ}$ intersecting $\parallel$ lines $\overline{XY}$ and $\overline{ZW}$).

Step2: Parallel lines imply congruent alt. int. angles

Since $\overline{XY} \parallel \overline{ZW}$, alternate interior angles are congruent.

Step3: Identify vertical angles

$\angle XVY$ and $\angle ZVW$ are vertical angles, so congruent.

Step4: Apply AA similarity theorem

Two pairs of congruent angles mean triangles are similar by AA.

Answer:

First blank: $\angle X$; Second blank: $\angle Z$; Third blank: congruent; Fourth blank: vertical; Fifth blank: AA (Angle-Angle)