Question

A line segment is sometimes/never/always similar to another line segment, because we can sometimes/never/always map one onto the other using only dilations and rigid transformations.

Answer 1

Answer: sometimes for both

Step-by-step explanation:

Answer 2

Answer: "always" for both

A line segment is always similar to another line segment, because we can always map one onto the other using only dilations and rigid transformations.

==================================

Explanation:

A dilation is where we grow or shrink an object. In this case, it would be lengthening or shortening a line. We can dilate any line to get it to any desired length we want. Then to make sure it matches up perfectly with the other line, we can perform translations (aka shifting) and rotations.

In other words, if we have four points A,B,C,D then it is possible to use dilations and rigid transformations to map points A,B to points C,D. The first segment AB would map to segment CD.