Triangle abc has been dilated to form triangle a'b'

c. if sides ab and a'b' are proportional, what is the least amount of additional information needed to determine if the two triangles are similar?

It is needed at least one more piece of information.

If you call k the ratio a'b' / ab, the addtional information may be tha cb' has the same ratio to cb or that ca' has the same ratio to ca.

It migh also be that the angle at the vertex C has not changed.