Answer:
Line RT || Line VS ∠SRV ≅ ∠TUR - Given/Alternate Interior Angles Theorem
∠TRU ≅ ∠SVR - Corresponding Angles Theorem
ΔRTU ~ ΔVSR - AA Similarity Theorem
Step-by-step explanation:
The statement Line RT || Line VS ∠SRV ≅ ∠TUR is given. This can be explained with the Alternate Interior Angles Theorem. It states that if two parallel lines (TR and VS) are cut by a transversal (∠SRV), then the pairs of alternate interior angles are congruent.
∠TRU and ∠SVR correspond to each other, so that would be the Corresponding Angles Theorem.
That leaves ΔRTU ~ ΔVSR being that away due to the AA Similarity Theorem. It states that states that if two angles of one triangle (∠RTU, ∠URT for example) are congruent to two angles of another triangle (∠VSR, ∠RVS are the congruent angles to the two from before), then the triangles are similar.
