Definition
Perpendicular bisector
A line that crosses a segment at its midpoint and at a right angle.
What it means
A perpendicular bisector does two jobs at once: it cuts a segment into equal halves and crosses it squarely. Imagine a straight line standing at a perfect right angle on the segment’s exact middle.
Remember it
Two checks: halfway and squarely—equal halves at 90°.
Example
If AB is 10 cm long and line ℓ is its perpendicular bisector, ℓ meets AB 5 cm from A and 5 cm from B, at a right angle.
Watch for
A line through the midpoint that is not at 90°, or a 90° line that misses the midpoint, is not the perpendicular bisector.
Common mix-up
An angle bisector splits an angle into equal angles; a perpendicular bisector splits a segment and crosses it at 90°.
Exact meaning
The perpendicular bisector of a line segment is the line that passes through the segment’s midpoint at 90°; every point on that line is equally distant from the segment’s two endpoints.