A transformation doesn't distort. Presumably by "composition" you mean composition of functions. If so, take a triangle, and take the function which sends every point (x,y) on the triangle to the point (x,0), then compose this with the function which leaves every point alone (the trivial mapping). The composition of these two functions distorts the triangle and thus is not a transformation.
I fear I may be misunderstanding what you have in mind when you say "composition".