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
diagram
congruence statement
method
\\( \overline { q u } \cong \overline { p s } \\)
\\( \triangle p q u \cong \triangle \\)
vrs
i

Explanation:

Step1: Identify corresponding parts

From the diagram, we can observe that \(\angle QPU\cong\angle SVU\) (given by the angle markings), \(\overline{QU}\cong\overline{PS}\) (given), and \(\angle PQU\cong\angle VSP\) (given by the angle markings).

Step2: Apply congruence postulate

The Angle - Angle - Side (AAS) congruence postulate states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

AAS