Copy an angle

The question

Copy angle ABC onto the ray from D.

How it works.

compass+straightedge

Step 1→With the point on B, draw an arc crossing both arms of the angle

Step 2→Keeping that opening, draw the same arc from D, crossing the ray

Step 3→Set the compass to the distance between the two crossings on the first arc

Step 4→Step that distance round from where the second arc meets the ray, and draw the arm through it

arcs=the evidence

01
Copy angle ABC onto the ray from D. Use only a compass and a straightedge — no measuring.
02
1. With the point on B, draw an arc crossing both arms of the angle. Now the angle is marked by two points the same distance from B.
03
2. Keeping that opening, draw the same arc from D, crossing the ray. Same opening, so the new arc matches the old one.
04
3. Set the compass to the distance between the two crossings on the first arc. This distance is the gap between the two arms at that radius — the one thing left that fixes the angle.
05
4. Step that distance round from where the second arc meets the ray, and draw the arm through it. The two triangles now have three equal sides (SSS), so the angles at B and D are equal.
06
Leave every arc showing — they show how the figure was made.