Question

segment gr is congruent to segment ln. true false

Explanation:

Step1: Analyze triangle congruence

To check if \(GR\cong LN\), we need to see if \(\triangle BGR\) and \(\triangle LNC\) are congruent.
In \(\triangle BGR\), we have side - side - angle (SSA) is not a valid congruence criterion. But if we assume the triangles are congruent based on the markings (if we consider proper congruence rules like ASA, SAS, SSS etc. mis - application here as per the given figure's markings). Wait, no, actually, in \(\triangle BGR\), the sides adjacent to \(\angle B\) and \(\angle R\) and in \(\triangle LNC\), the sides adjacent to \(\angle N\) and \(\angle C\) are not in the same proportion for congruence.
Let's use the concept of triangle congruence. If two triangles are congruent, then their corresponding sides are congruent. But here, the triangles do not satisfy any of the congruence rules (SSS: \(BG
eq LN\), \(BR
eq NC\), \(GR
eq LC\); SAS: the included angles are not equal; ASA: the angles and included sides are not equal). So \(GR\) and \(LN\) are not corresponding sides of congruent triangles.

Answer:

False