In geometry, to bisect is to divide a geometric figure such as a line, an angle or any other shape into two congruent parts (or two parts that have the same shape and size).
You could bisect a segment with a point
Since point A divides the segment into two parts that have the same size and shape, the segment is bisected.
You could bisect an angle with a ray
Since ray AB divides the angle into two parts that have the same size and shape, the angle is bisected.