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 the given information

From the figure, we can assume that \(PG = PJ\) (marked with one tick), \(GN=JN\) (marked with two ticks), and \(PN\) is common to both \(\triangle PGN\) and \(\triangle PJN\).

Step2: Recall SSS congruence criterion

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.
In \(\triangle PGN\) and \(\triangle PJN\), we have \(PG = PJ\), \(GN=JN\), and \(PN = PN\) (common side).

Answer:

The triangles are congruent by SSS Congruence.