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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.

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Converse of the Perpendicular Bisector Theorem - if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.Example: If DA = DB, then point D lies on the perpendicular bisector of line segment AB.you :))

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?

A segment need not be a bisector. No theorem can be used to prove something that may not be true!

They are the same concept, one for the angle and 1 for triangle.Definition of a triangle angle bisector is a line segment that bisects one of the vertex angles of a triangle.Definition of an angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.

Yes

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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 equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.Example: If DA = DB, then point D lies on the perpendicular bisector of line segment AB.you :))

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?

A segment need not be a bisector. No theorem can be used to prove something that may not be true!

a point on the bisector of an angle, it is equidistant from the 2 sides of the angle

The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.

They are the same concept, one for the angle and 1 for triangle.Definition of a triangle angle bisector is a line segment that bisects one of the vertex angles of a triangle.Definition of an angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.