Math Help - affine transformation invariant

1. affine transformation invariant

hello,
if we transform few triangles by affine transformation, the transformed triangle will change its shape, but what is the quantity, the measurement, or the proportion that is still invariant?

OR
what's the relation R, between f(A,B,C) and g(A',B',C')

where f is before transform, g is after,

if someone says its cross ratio that still invariant,so how could we prove that using an affine transform equation?

thanx