Given: XY || ZW Prove: △XYV ~ △ZWV

Triangles X V Y and W V Z are connected at point V. Sides X Y and W Z are parallel.

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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.