Geometry- Theorem 5-1

perpendicular bisector theorem

if a point is on the perpendicular bisector of a segment

Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long.

midsegment of a triangle

a line that joins the midpoints of two sides of a triangle

equidistant

at equal distances

converse of the angle bisector theorem

if a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

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.

Angle bisector theorem

if a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

concurrency of perpendicular bisectors theorem

the perpendicular bisectors of the sides of a triangle are congruent at a point equidistant from the verticies