What is the defining feature of a perpendicular bisector?

The defining feature of a perpendicular bisector is that it divides a line segment into two equal lengths and forms right angles with it. This means that if you have a line segment, the perpendicular bisector will cut it precisely in half, creating two segments of equal length. Additionally, the angle formed between the bisector and the original line segment is exactly 90 degrees, which is characteristic of perpendicular lines.

This property is essential in many geometric constructions and proofs, such as when finding the circumcenter of a triangle, where the perpendicular bisectors of the sides intersect at a point that is equidistant from all three vertices. Understanding this concept helps students grasp the relationships between different geometric figures and their properties.