a parallelogram does not have a line of symmery
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A line segment having end points is one possibilty others are:-
Parallel lines
Perpendicular line
Intersecting lines
Transversal line
Straight line equation
A geometrical straight line is infinite but if it has defined end points then it is a line segment.
A geometrical object that is straight, infinitely long and infinitely thin.
It is a geometrical construction
Not sure about a lie, but such a line is called the diameter.
A line, "living" in N-dimensional space, where N is the number of variables.