What defines concurrent triangles?

Concurrent triangles are defined as triangles that share one side and have their other angles congruent, resulting in the triangles being similar. Therefore, while similar triangles have proportional sides and identical internal angles, concurrent triangles also maintain a shared side, which distinguishes them from identical triangles.

In the context of the provided choices, "triangles which are identical" suggests that every side and angle is the same, indicating that they are not just similar but exactly the same. This definition aligns with the concept of identity in geometric terms, where both shape and size are congruent.

While sharing one side is a defining characteristic of concurrent triangles, identity requires more specific equality in dimensions and angles, making identical triangles a more constrained case. This understanding helps clarify the distinct attributes that can be present in triangles classified as concurrent.

Thus, identifying concurrent triangles means recognizing the defining relationship of sharing one side while also considering their similarity due to congruent angles, which enhances understanding of triangle relationships in geometry.