Perpendicular bisector

The question

Construct the bisector of AB.

How it works.

compass+straightedge

Step 1→Open the compass to more than half of AB

Step 2→With the point on A, draw arcs above and below the segment

Step 3→Keeping the same opening, do the same from B

Step 4→Draw the line through the two crossings. It cuts AB in half, at a right angle

arcs=the evidence

01
Construct the bisector of AB. Use only a compass and a straightedge — no measuring.
02
1. Open the compass to more than half of AB. Less than half and the two arcs would never meet.
03
2. With the point on A, draw arcs above and below the segment. Every point on this arc is the same distance from A.
04
3. Keeping the same opening, do the same from B. Same opening, so every point on this arc is that distance from B. Where the arcs cross, a point is equally far from A and B.
05
4. Draw the line through the two crossings. It cuts AB in half, at a right angle. Every point equally far from A and B lies on the perpendicular bisector, so two such points are enough to draw it.
06
Leave every arc showing — they show how the figure was made.