A triangle is made up of vertices upper A, upper B, and upper C. Another triangle is made up of vertices upper P, upper Q, and upper R. Angles upper C, upper A, upper Q, and upper R are marked by arcs.

Question

What missing piece of information would make △ABC≅△RPQ
by AAS?

(1 point)
Responses

AC¯¯¯¯¯¯¯¯≅RQ¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar congruent to Modifying above upper R upper Q with bar

BC¯¯¯¯¯¯¯¯≅PQ¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper P upper Q with bar

∠B≅∠P
angle upper B congruent to angle upper P

∠B≅∠C

Answer 1

To prove that triangles \( \triangle ABC \) and \( \triangle RPQ \) are congruent by the AAS (Angle-Angle-Side) postulate, we need two angles and the included side (or a non-included side) of one triangle to be congruent to the corresponding parts of the other triangle.

The marked angles indicate that we have \( \angle C \) and \( \angle A \) in triangle \( ABC \), and \( \angle Q \) and \( \angle R \) in triangle \( RPQ \) that are congruent. To satisfy the AAS criterion, we need one additional angle or a side that connects these triangles.

Among the options provided, the third option:

∠B≅∠P

would provide the necessary information to complete the AAS condition for triangle \( ABC \) and triangle \( RPQ \).

So, the missing piece of information that would make \( \triangle ABC \cong \triangle RPQ \) by AAS is:

∠B≅∠P (angle B congruent to angle P).