Question

which of the following describes the relationship between the given triangles? none of these △pnm≅△abc by the asa congruence theorem △pmn≅△bac by the asa congruence theorem △pnm≅△abc by the aas congruence theorem

Explanation:

Step1: Recall ASA and AAS congruence theorems

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent.

Step2: Identify congruent parts in triangles

In \(\triangle PMN\) and \(\triangle BAC\), we can see that \(\angle M=\angle A\), \(MN = AC\) (marked with single tick), and \(\angle N=\angle C\). This is two angles and the included side, so we use ASA congruence. Also, the correct way to write the congruence of triangles is by matching the corresponding vertices. So \(\triangle PMN\cong\triangle BAC\) by ASA.

Answer:

\(\triangle PMN\cong\triangle BAC\) by the ASA congruence theorem