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Constructing an Angle Bisector

Remember that an angle bisector is a ray whose endpoint is the vertex of an angle and that splits the angle into two congruent parts (i.e. they have the same angle measure). To construct the bisector of an angle do the following:

  1. Start with an angle.
  1. Put your compass on the vertex and drawn an arc that cuts across both sides.
  1. Now put your compass on one of the points where your arc crosses a side and draw a second arc inside the angle.
  1. Repeat step three but with the point where your arc crosses the other side of the angle.
  1. Now use your straightedge to draw a ray connecting the vertex with the point where the arcs you drew in steps 3 and 4 cross. That ray is the bisector of your original angle.