A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.
It depends on how it's used. For example if it's angles it could be because of Vertical Angles. If it's Triangles it could be Definition of Congruent Triangles.
