perpendicular bisector
a segment, ray, line, or plane that is perpendicular to a segment at its midpoint
A perpendicular bisector is a line or a segment that passes through the midpoint of a given segment and divides it into two equal halves. Additionally, the line or segment must be perpendicular to the given segment. In other words, it creates a right angle with the given segment and intersects it at its midpoint.
For example, let’s consider the segment AB. We can draw a line or segment that passes through the midpoint of AB and makes a right angle with it. This line or segment is the perpendicular bisector of AB. It would divide AB into two equal halves and would be equidistant from points A and B.
The perpendicular bisector has a variety of applications in geometry, including in construction problems and in finding the center of a circle. It is also commonly used in proving theorems, such as the Triangle Midsegment Theorem, which states that the perpendicular bisector of a side of a triangle is also the midsegment of the triangle.
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