Triangle Centers and Concepts

Circumcenter

Intersection of perpendicular bisectors; center of the circumcircle; equidistant from vertices.

Incenter

Intersection of angle bisectors; center of the incircle; equidistant from sides.

Centroid

Intersection of medians; center of mass; divides medians in a 2:1 ratio.

Orthocenter

Intersection of altitudes; no distance properties; can be inside, on, or outside the triangle.

Median

Segment from a vertex to the midpoint of the opposite side.

Altitude

Perpendicular segment from a vertex to the opposite side.

Angle Bisector

Segment that splits an angle into two equal parts.

Perpendicular Bisector

Line that is perpendicular to a segment at its midpoint.