In geometry (or math in general), when you do a reflection, rotation, or translation the size or length of the lines don't change. Think about it this way: if I have a log and I bring it into the bathroom with me (don't ask why idk) and hold it up in from of the mirror, what will happen? It will look the same length (and people will think I'm crazy for bringing a log into the restroom with me... but I digress).
A reflection across a line is a rigid transformation. Therefore the shape of the original object will not change. Because of this, you know that it would have the same length as the original line segment.
