Since VU is parallel to SR we can use the Alternate Interior Angles Theorem. According to this theorem, if parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. This means that ∠ TUV= ∠ TSR and ∠ TVU= ∠ TRS.
Now, let's recall that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This postulate is called Angle-Angle Similarity Theorem. Since the triangles have all three angles congruent we can say that △ TVU ~ △ TRS by AA Similarity Theorem.
