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With a straight-edge and a compass:

  1. Swing arcs from each end of the segment with the compass (without changing the settings)
  2. Connect the intersections of these arcs.
The resultant is a perpendicular bisector of the segment.
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Q: What must you do to construct the midpoint of a segment?
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If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the segment?

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