Question

shown are sx, vz and pq. pq is intersecting sx at point y and vz at point t. if ∠syp≅∠vty, then sx∥vz because of the converse of the alternate interior angles theorem. converse of the consecutive interior angles theorem. converse of the corresponding angles theorem. no conclusion can be made.

Explanation:

Step1: Identify angle relationship

$\angle SYP$ and $\angle VTY$ are alternate - interior angles formed by lines $\overleftrightarrow{XY}$ and $\overleftrightarrow{VZ}$ with transversal $\overleftrightarrow{PQ}$.

Step2: Apply theorem

If alternate - interior angles are congruent, by the converse of the alternate - interior angles theorem, the lines are parallel. So, if $\angle SYP\cong\angle VTY$, then $\overleftrightarrow{XY}\parallel\overleftrightarrow{VZ}$.

Answer:

Converse of the alternate - interior angles theorem.