Question

developing proof state the third congruence that must be given to prove that △pqr ≅ △stu using the indicated postulate or theorem. (hint: first sketch △pqr and △stu. mark the triangles with the given information.) 14. given ▶ ∠q ≅ ∠t, pq ≅ st use the aas congruence theorem.

Explanation:

Step1: Recall AAS Congruence Theorem

AAS (Angle - Angle - Side) Congruence Theorem 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.

Step2: Identify the given congruences

We are given \(\angle Q\cong\angle T\) and \(\overline{PQ}\cong\overline{ST}\). For AAS, we need another pair of angles.

Step3: Determine the required angle

Since \(\overline{PQ}\) and \(\overline{ST}\) are non - included sides with respect to \(\angle Q\) and \(\angle T\), we need \(\angle R\cong\angle U\)

Answer:

\(\angle R\cong\angle U\)