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Here are 2 points labeled and , and a line segment :
Use the tools available to find the perpendicular bisector of segment .
After coming up with a method, make a copy of segment on tracing paper and look for another method to find its perpendicular bisector.
A perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it. Recall that a right angle is the angle made when we divide a straight angle into two congruent angles. Lines that intersect at right angles are called perpendicular.
A conjecture is a guess that hasn't been proven yet. We made a conjecture that the perpendicular bisector of segment is the set of all points that are the same distance from as they are from . This turns out to be true. The perpendicular bisector of any segment can be constructed by finding points that are the same distance from the endpoints of the segment. Intersecting circles with the same radius centered at each endpoint of the segment can be used to find points that are the same distance from each endpoint, as circles show all the points that are a given distance from their center point.
A conjecture is a reasonable guess that someone is trying to either prove or disprove.
The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to the segment.
In this diagram, the dashed line is the perpendicular bisector of segment .