Final answer:
The given statement 'If triangles have two angles and one side congruent, but the side is not between the angles, then the triangles are not necessarily congruent' is false.
Step-by-step explanation:
It is inaccurate to say that triangles are inherently not congruent if they have two angles and a side that is congruent but the side is not between the angles.
For example, let's consider two triangles ABC and DEF where angle A and angle D are congruent, angle B and angle E are congruent, and side AB is congruent to side DE.
However, if side BC is not congruent to side EF, then the triangles ABC and DEF are not congruent.