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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.

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step-by-step explanation:

(-5,-28)

i graphed to on desmos.