Step-by-step explanation:
∠YXZ and ∠VXU are vertical angles, and therefore are congruent.
<em>∠YXZ ≅ ∠VXU, Vertical ∠'s ≅</em>
Next, we're given that lines YZ and UV are parallel. That means that ∠YZV and ∠UVZ are alternate interior angles, and therefore congruent.
<em>∠YZV ≅ ∠UVZ, If lines ||, then alternate interior ∠'s ≅</em>
If two triangles have two pairs of congruent angles, then the third pair must also be congruent, making the two triangles similar.
<em>△XYZ ~ △XUV, AA</em>
Since the triangles are similar, then by definition, their sides are proportional.
<em>XY/XU = YZ/UV, Definition of Similar Polygons</em>
