Theorem 111. Dilations preserve angle measure. Specifically, if non- collinear points A, B and C go to (necessarily) non-collinear points A', B' and C' under a dilation, then LABC LA'B'C'. [Draw a diagram and apply what you know.] The definition of a dilation says that the length of each segment coming from the center O is multiplied by the scaling factor k, that is, L(OP)=kL(OP). We would like to find out if the same relationship holds for every segment.