Fundamental Concepts
8. Perpendicular Bisector · always at right angles, exactly in the center
The constructed line always passes through the midpoint and stays perpendicular to AB.
The perpendicular bisector of segment AB passes through its midpoint M and meets AB at a right angle (90°). Every point on it is equidistant from A and B. Drag A or B — M, the bisector, and the right angle all update together.
What this lesson covers
Try to break it
Try moving A and B very close together. Does the bisector still work? Absolutely—it's always unique and perfectly perpendicular!
How you build it
Construct the perpendicular bisector of AB.
- Place point A on the left.
- Place point B on the right.
- Draw segment AB.
- Open the Compass to length AB and swing an arc from A (click A, then B).
- Swing a matching arc from B (click B, then A). The two arcs cross above and below AB.
- Draw the line through both arc intersections — that''s the perpendicular bisector of AB.
The proof, step by step
Prove that the constructed line is the perpendicular bisector of AB.
- The bisector passes through the midpoint M of segment AB.
- The bisector is perpendicular to AB, forming 90° angles at M.
- Every point on the perpendicular bisector is equidistant from A and B.
Worked example
Line l is the perpendicular bisector of line segment AB. If point P lies on line l, which of the following is true?
By the perpendicular bisector theorem, any point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
- PA = PB — correct
- PA > PB
- PA < PB
- PA + PB = AB