Question

statement reason 1 ∠sru ≅ ∠rut given 2 ∠prq ≅ ∠sru vertical angle theorem 3 ∠rut ≅ ∠prq transitive property of congruence 4 qs||tv

Explanation:

Step1: Identify given congruent angles

We are given that $\angle SRU\cong\angle RUT$.

Step2: Use vertical - angle theorem

By the vertical - angle theorem, $\angle PRQ\cong\angle SRU$ since they are vertical angles.

Step3: Apply transitive property

Since $\angle SRU\cong\angle RUT$ and $\angle PRQ\cong\angle SRU$, by the transitive property of congruence, $\angle RUT\cong\angle PRQ$.

Step4: Determine parallel lines

If $\angle RUT\cong\angle PRQ$, then $QS\parallel TV$ because alternate - interior angles are congruent, which implies parallel lines.

Answer:

The reason for $QS\parallel TV$ is that alternate - interior angles $\angle RUT$ and $\angle PRQ$ are congruent.