Question

based on the given information in the diagram, what additional information is needed to prove \\( \triangle abc \cong \triangle rpq \\) by the aas congruence theorem? (1 point) \\( \angle b \cong \angle p \\) \\( \overline{bc} \cong \overline{pq} \\) \\( \overline{ac} \cong \overline{rq} \\)

Explanation:

Step1: Recall AAS Congruence Theorem

AAS (Angle - Angle - Side) 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 triangles are congruent.
In \(\triangle ABC\) and \(\triangle RPQ\), we already have \(\angle A=\angle R = 40^{\circ}\) and \(\angle C=\angle Q=91^{\circ}\).

Step2: Identify the non - included side

For AAS, we need a pair of non - included sides to be congruent.
The non - included side for \(\angle A\) and \(\angle C\) in \(\triangle ABC\) is \(BC\), and the non - included side for \(\angle R\) and \(\angle Q\) in \(\triangle RPQ\) is \(PQ\). But if we consider another pair, the non - included side for \(\angle A\) and \(\angle C\) can also be \(AC\), and the non - included side for \(\angle R\) and \(\angle Q\) is \(RQ\).

Answer:

\(\overline{AC}\cong\overline{RQ}\)