Question

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Explanation:

Step1: Identify Triangle Congruence

We have two angles and the included side for triangles \( \triangle QST \) and \( \triangle RSQ \). From steps 1, 2, and 3, \( \angle QST \cong \angle RQS \), \( \angle QSR \cong \angle SQT \), and \( \overline{QS} \cong \overline{QS} \). By ASA (Angle - Side - Angle) Congruence Criterion, \( \triangle QST \cong \triangle RSQ \).

Step2: Corresponding Parts of Congruent Triangles

Since \( \triangle QST \cong \triangle RSQ \), their corresponding sides \( \overline{QT} \) and \( \overline{RS} \) are congruent. So the statement for step 4 is \( \triangle QST \cong \triangle RSQ \) (by ASA) and then we can conclude \( \overline{QT} \cong \overline{RS} \) as corresponding parts of congruent triangles are congruent (CPCTC). But for the statement in step 4, we need to state the triangle congruence. So the statement is \( \triangle QST \cong \triangle RSQ \) and the reason is "ASA (Angle - Side - Angle) Congruence Postulate" (because we have two angles and the included side congruent: \( \angle QST \cong \angle RQS \), \( \overline{QS} \cong \overline{QS} \), \( \angle QSR \cong \angle SQT \)). Then, from the congruence of triangles, we get \( \overline{QT} \cong \overline{RS} \) by CPCTC. But focusing on step 4's statement, we need to show the triangle congruence.

Answer:

Statement 4: \( \triangle QST \cong \triangle RSQ \); Reason: ASA (Angle - Side - Angle) Congruence Postulate (and then by CPCTC, \( \overline{QT} \cong \overline{RS} \))