Q: What is the converse of the perpendicular bisector theorem?

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The converse of perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

The Angle Bisector Theorem states that given triangle and angle bisector AD, where D is on side BC, then . Likewise, the converse is also true. Not sure if this is what you want?

An angle bisector bisects an angle. A perpendicular bisector bisects a side.

A circle cannot form a perpendicular bisector.

A circle can have perpendicular bisector lines by means of its diameter.

Related questions

The converse of perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Biconditional Statement for: Perpendicular Bisector Theorem: A point is equidistant if and only if the point is on the perpendicular bisector of a segment. Converse of the Perpendicular Bisector Theorem: A point is on the perpendicular bisector of the segment if and only if the point is equidistant from the endpoints of a segment.

converse of the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant, or the same distance, from the endpoints of the segment.

converse of the angle bisector theorem

No, it does not.

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle-apex

The Angle Bisector Theorem states that given triangle and angle bisector AD, where D is on side BC, then . Likewise, the converse is also true. Not sure if this is what you want?

An angle bisector bisects an angle. A perpendicular bisector bisects a side.

A circle cannot form a perpendicular bisector.

on the perpendicular bisector

The Perpendicular bisector concurrency conjecture is the circumcenter