Question

complete the triangle congruence statement in order to prove the given statement
what postulate or theorem would you use (sss, sas, hl, aas or asa)?
given
\\( \overline { qu } \cong \overline { ps } \\)
diagram
congruence statement
\\( \triangle pqu \cong \triangle \\)
method

Explanation:

Step1: Identify corresponding parts

From the diagram, we have \( \overline{PU}\cong\overline{PS}\) (given \( \overline{QU}\cong\overline{PS}\), assume \(PU = QU\) as per congruent triangles' side - angle - side relation if we consider the common side \(PQ\)). Also, \( \angle QPU=\angle SPU\) (the two angles marked as equal in the diagram). And \(PQ\) is a common side.

Step2: Apply congruence criterion

For \(\triangle PQU\) and \(\triangle PSS\), we have two sides and the included angle equal. By the Side - Angle - Side (SAS) congruence criterion.

Answer:

Congruence Statement: \(\triangle PQU\cong\triangle PSS\)
Method: SAS