Question

use the image to answer the question. based on the given information in the diagram, what additional information is needed to prove △abc≅△rpq by the aas congruence theorem? enter the number of the correct option. option #1 ac≅rq option #2 ∠b≅∠p option #3 bc≅pq (1 point)

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.
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 sides

The non - included sides for the given pairs of angles are \(BC\) and \(PQ\). For \(\triangle ABC\cong\triangle RPQ\) by AAS, we need \(BC\cong PQ\).

Answer:

Option #3 \(BC\cong PQ\)