Question

given xy || zw prove △xyv ~ △zwv use the drop - down menus to complete the paragraph proof we are given that xy is parallel to zw if xz is a transversal that intercepts xy and zw, angle and angle are alternate interior angles since xy is parallel to zw, we know that these angles are we also know that angle xvy and angle zvw are angles, and thus congruent. we can conclude that △xyv ~ △zwv using the similarity theorem

Explanation:

• When \( \overline{XY}\parallel\overline{ZW}\) and \( \overline{XZ}\) is a transversal, by the alternate - interior angles theorem, \( \angle X\) and \( \angle Z\) are alternate - interior angles and are congruent.
• \( \angle XVY\) and \( \angle ZVW\) are vertical angles (opposite angles formed by the intersection of two lines), and vertical angles are congruent.
• In the AA (Angle - Angle) similarity theorem, if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Here, in \( \triangle XYV\) and \( \triangle ZWV\), we have two pairs of congruent angles (\( \angle X\cong\angle Z\) and \( \angle XVY\cong\angle ZVW\)), so \( \triangle XYV\sim\triangle ZWV\) by the AA similarity theorem.

Answer:

1. \( \angle X\)
2. \( \angle Z\)
3. congruent
4. vertical
5. AA (Angle - Angle)