Copy a segment

The question

Copy AB onto the ray from C.

How it works.

compass+straightedge

Step 1→Open the compass so its point is on A and its pencil is on B

Step 2→Keeping that opening, put the point on C and draw a short arc crossing the ray

Step 3→Label the crossing D. CD is the same length as AB

arcs=the evidence

01
Copy AB onto the ray from C. Use only a compass and a straightedge — no measuring.
02
1. Open the compass so its point is on A and its pencil is on B. The compass now holds the length of AB — no ruler needed.
03
2. Keeping that opening, put the point on C and draw a short arc crossing the ray. Moving the compass does not change its opening, so every point on this arc is exactly |AB| from C.
04
3. Label the crossing D. CD is the same length as AB. D is on the arc and on the ray, so CD = AB exactly.
05
Leave every arc showing — they show how the figure was made.