Is the point order of the triangles really relevant when it comes to congruence?
Let us assume that: $\triangle ABC \cong \triangle DEF$
Which means that there is a congruence correspondence $ABC \longleftrightarrow DEF$. Intuitively I'd say that $\triangle CBA \cong \triangle DEF$ as well because we're dealing with the same triangles.
I'm currently working myself through Geometry by Harold R. Jacobs. In it the definition of congruence is:
Two angles are congruent iff there is a correspondence between their vertices such that the corresponding sides and corresponding angles of the triangles are equal.
In the book the author states that if $\triangle GHI \cong \triangle LKJ$, then there is a correspondence $GHI \longleftrightarrow LKJ$, but there is no correspondence $GHI \longleftrightarrow JKL$ therefore we cannot write $\triangle GHI \cong \triangle JKL$. ($\triangle GHI$ and $\triangle LKJ$ are neither isosceles, nor equilateral in this specific example).
Is this really the case?