If they have the same length.
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A bisector cuts a line SEGMENT into two congruent line segments. A line has indefinite or infinite length.
no
yes
Congruent can mean corresponding to (or agreeing with); or in mathematics, it can mean identical in shape and size. For example, two circles are congruent if they have the same size, while two line segments are congruent if they have the same length. So it basically means that it has the same shape and size.
Two things are congruent if they are the same shape and size.