A line that does not have a vertex on one side (continues to grow from one end) is called a ray.
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A line segment ends, because it is a line with two dots on the end to stop it. It is just a regular line that does not end. There could also be a ray, which is a line with only one side stopped with a point and the other going on forever. you said it ends and then you said it doesn't end
It is an edge.
A ray is different from a segement because a ray is half of a line and does not end in one side only but the segement it is half of a line that ends.
It's called a side or edge.
The hidden line is drawn, however, the edges of the center line can still be seen ( the center line ends up appearing as extra long dashes on either side of the end of the hidden line)