What kinda math is this

When we do a translation, all the translated points must be translated in parallel (between them) lines. (this would mean that all our points suffer the same translation)

Here we can see that the lines BB´ and AA´ are parallel, but the line CC´ is not parallel to the other two. So the distance of the translation is constant, but the direction is not the same for all the points.

Then this is not a translation of all our triangle, because different points suffered different translation operations, this is what caused the triangles ABC and A´B´C´ to not be congruent.