Ruler and Compass Construction 10
Bisector of a Given Angle

1. Circle centered at A of arbitrary radius
2. Circle centered at D of arbitrary radius
3. Circle centered at E of the same radius
4. Angle bisector AF
Why it works: AD = AE and DF = EF by construction, and AF = AF by reflexivity, so triangle ADF is congruent to triangle AEF by SSS. Hence angle DAF equals angle EAF.
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