Question

selective which triangle congruence criteria should be used to prove the two triangles are congruent. which of these statements is correct? the triangles are congruent by sss congruence. the triangles are congruent by asa congruence. the triangles are congruent by sas congruence. the triangles are congruent by aas congruence.

Explanation:

Step1: Analyze SSS Congruence

SSS (Side - Side - Side) requires three pairs of corresponding sides to be equal. Here, we don't have information about all three sides for a clear SSS case.

Step2: Analyze ASA Congruence

ASA (Angle - Side - Angle) is not applicable as we don't have two angles and the included side information.

Step3: Analyze SAS Congruence

SAS (Side - Angle - Side) is the correct criterion. Let's assume \(PG = PJ\) (marked as equal), \(GN=JN\) (marked as equal) and \(\angle PGN=\angle PJN\) (common angle at \(P\) and the angles formed by the equal sides).

Step4: Analyze AAS Congruence

AAS (Angle - Angle - Side) is not relevant as we have a side - angle - side situation.

Answer:

The triangles are congruent by SAS Congruence.