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Suppose you need to bisect angle PQR using only a pair of compasses and a straight edge:

  1. Draw an arc with the point of the compass at Q so the arc QP at X and QR at Y.
  2. Draw an arc with the point of the compass at X so that the arc is between the arms of the angle and extends to more than halfway across.
  3. Without changing the compass setting, draw an arc with the point of the compass at Y so that this arc intersects the previous arc at Z.
  4. Using the straight edge, draw the line QZ: this is the bisector of angle PQR.
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Q: What are the proper steps for constructing an angle bisector?
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