What Is the Perpendicular Bisector Theorem?


Quick Answer

The perpendicular bisector theorem is applicable for line segments. The theorem states that the perpendicular bisector is a line that represents the locus of points that are equidistant from the endpoints of the line segment that it intersects.

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Full Answer

As its name suggests, a perpendicular bisector intersects a line segment in a right angle and in such a way that it cuts the line segment into two equal parts. The theorem is often mentioned in similar theorems and laws of analytic geometry, particularly in triangles and circles. For triangles, the perpendicular bisectors of the three sides of the triangle intersect at a common point that is equidistant to the three vertices. In circles, the theorem may be used to pinpoint the location of the center by choosing three random points on the circle and connecting these points with line segments. The perpendicular bisectors of these three line segments will converge at a point that coincides with the circle's center.

Any line segment has an infinite number of bisectors but only a single perpendicular bisector. To illustrate a line segment's perpendicular bisector on paper, the length of the line segment must be measured. This length should be divided into two, and the point of division is the intersecting point of the bisector. From this point, a 90-degree angle should be measured and the bisector line projected from this angle.

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