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Constructing Perpendicular Bisectors in Geometry

In geometry, a perpendicular bisector is a line that cuts another line segment into two equal pieces. The bisector is perpendicular to (forms a right angle with) the segment it bisects. You can construct (draw) a perpendicular bisector of a given line segment using only a compass and straightedge (ruler). This process is sometimes called "taking measurements."

Here's how to do it:

  1. Draw the given line segment. Make sure it's long enough so that the compass can fit comfortably on each endpoint.
  2. Place the point of the compass on one endpoint of the segment and open the compass to any radius. Swing an arc above and below the segment.
  3. Place the point of the compass on the other endpoint of the segment and swing another arc intersecting the first arc. Mark both points of intersection. These are your "center" points.
  4. With the compass still open to the same radius, place its point on one of your center points. Swing an arc through both endpoints of the original segment—your arcs should intersect at right angles (90 degrees). Mark both points of intersection; these are where your perpendicular line will go. Erase your Construction Arcs (temp lines). Now you have your perpendicular bisector!
  5. If you need to, use a ruler or protractor to check that your arcs intersect at 90 degrees, or that each endpoint of your original segment is equidistant from your newline—that is, if you measure one endpoint to Point A and then from Point A to Point B, that distance should be equal to measuring from the other endpoint straight across to Point B. If not, something's gone wrong—check your work and make sure all lines are construction lines (dashed or dotted), not part of your final figure!


That's all there is to it! Now you know how to construct perpendicular bisectors in geometry using only a compass and straight edge (ruler). As always, if you need any help or clarification, please don't hesitate to reach out to your teacher or tutor. Good luck!

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