Chapter 5: Special Segments and Triangle Centers

triangle midsegment

a segment connecting the midpoints of two sides of the triangles

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

perpendicular bisector theorem

If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

converse of he 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 a bisector of an angle, then the point is equidistant from the sides of the angle

converse of the angle bisector theorem

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

circumcenter

the perpendicular bisectors of the sides of a triangle intersect at this point

incenter

the angle bisectors of the angles of a triangle intersect here

median

a segment joining a vertex to the midpoint of the opposite side

centroid

The three medians of a triangle intersect at this point

the length from the vertex to the centroid is...

twice as long as the length from the centroid to the side

altitude

a segment joining a vertex to the opposite side so that it's perpendicular to that side

orthocenter

The three altitudes of a triangle intersect at this point