Answers
A is false, similar triangle sides are not the same, but they have the same ratio of dilation. Similar figures are not congruent.
B is false, a rigid transformation does not change the shape or size of the preimage. The non-rigid transformation will change the size but not the shape of the preimage.
C is false, similar means that the figures have the same shape, but not the same size.
Similar figures are not congruent.
D is true, if you dilate a line segment, the original line segment will always be parallel to (or on the same line as) the image. Dilation does not change any other characteristics of a shape, so Parallel lines are still parallel.