A line that intersects a given segment at right angles and divides it into two equal parts
perpendicular bisector theorem
If a point is on the perpendicular bisector of a segment, then the point equidistant from the endpoints of the segment.
converse of perpendicular bisector theorem
If a point is equidistant to the endpoints of a segment, then it is on the perpendicular bisector.
the circumcenter of a triangle is equidistant to the verticies of the triangle.
angle bisector theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
converse of angle bisector theorem
If a point is in the interior of an angle and it is equidistant from the sides of the angle, then it lies on the bisector of the angle.
Angle bisectors of a triangle intersect at a single point called an ________. The ______ is the center of the inscribed circle of the triangle.
circumcenter of a triangle
the point of concurrency of the three perpendicular bisectors of a triangle
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 half its length
triangle inequality theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.