Bisect an angle

The question

Bisect angle ABC.

How it works.

compass+straightedge

Step 1→With the point on B, draw an arc crossing both arms. Call the crossings P and Q

Step 2→With the point on P, draw an arc inside the angle

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

Step 4→Draw the line from B through where the two arcs cross. It halves the angle

arcs=the evidence

01
Bisect angle ABC. Use only a compass and a straightedge — no measuring.
02
1. With the point on B, draw an arc crossing both arms. Call the crossings P and Q. P and Q are the same distance from B.
03
2. With the point on P, draw an arc inside the angle. Every point on this arc is one distance from P.
04
3. Keeping the same opening, do the same from Q. Same opening from Q, so where the arcs cross is equally far from P and Q.
05
4. Draw the line from B through where the two arcs cross. It halves the angle. B and the crossing are both equally far from P and Q, so the line through them splits the figure into two mirror halves — it halves the angle.
06
Leave every arc showing — they show how the figure was made.