Question

complete the proof that ( \triangle qrscong\triangle stq ).

statement	reason
2 ( overline{st}paralleloverline{qr} )	given
3 ( angle rqscongangle qst )	alternate interior angles theorem
4 ( overline{qs}congoverline{qs} )	reflexive property of congruence
5 ( \triangle qrscong\triangle stq )

Explanation:

Step1: Identify congruent parts

We have $\angle T \cong \angle R$ (given), $\angle QRS \cong \angle QST$ (alternate interior angles), and $\overline{QS} \cong \overline{QS}$ (reflexive property).

Step2: Apply congruence rule

Two angles and a non-included side of $\triangle QRS$ are congruent to the corresponding two angles and non-included side of $\triangle STQ$.

Answer:

AAS Congruence Theorem