Copy a segment, step by step

The first construction anyone learns.

The question
Copy AB onto the ray from C.ABC

Copy AB onto the ray from C.

Copy AB onto the ray from C.

compass+straightedge
Step 1Open the compass so its point is on A and its pencil is on B
Step 2Keeping that opening, put the point on C and draw a short arc crossing the ray
Step 3Label the crossing D. CD is the same length as AB
arcs=the evidence
  1. Copy AB onto the ray from C. Two tools only — a compass that holds a distance and a straightedge that draws a line. Nothing here is measured.
  2. 1. Open the compass so its point is on A and its pencil is on B. Opening the compass to A and B stores the length. Nothing is measured and nothing is written down — the distance itself is now held between the two points of the tool.
  3. 2. Keeping that opening, put the point on C and draw a short arc crossing the ray. Moving the compass does not change what it holds, so the arc you swing from C is exactly |AB| away from C, all the way round.
  4. 3. Label the crossing D. CD is the same length as AB. Where that arc meets the ray is the only point on the ray at distance |AB| from C. That is what makes D exact rather than close.
  5. Leave every arc showing. The arcs are the evidence the figure was constructed rather than eyeballed, and a marker reads them to check the method as well as the result.

How it works.

  1. 01

    Copy AB onto the ray from C. Two tools only — a compass that holds a distance and a straightedge that draws a line. Nothing here is measured.

  2. 02

    1. Open the compass so its point is on A and its pencil is on B. Opening the compass to A and B stores the length. Nothing is measured and nothing is written down — the distance itself is now held between the two points of the tool.

  3. 03

    2. Keeping that opening, put the point on C and draw a short arc crossing the ray. Moving the compass does not change what it holds, so the arc you swing from C is exactly |AB| away from C, all the way round.

  4. 04

    3. Label the crossing D. CD is the same length as AB. Where that arc meets the ray is the only point on the ray at distance |AB| from C. That is what makes D exact rather than close.

  5. 05

    Leave every arc showing. The arcs are the evidence the figure was constructed rather than eyeballed, and a marker reads them to check the method as well as the result.