COPY THIS: TOPIC: POINTS OF CONCURRENCY Some new vocabulary

DEFINITION: Concurrent Lines that contain the same point.

ORTHOCENTER The point where all the ALTITUDES of a triangle concur (meet, intersect). Acute – located inside Right – located on **Obtuse – located outside

Incenter The point where all the ANGLE BISECTORS concur(meet, intersect). The point of concurrence is the center of an inscribed circle. Acute – inside Right – inside Obtuse - inside

centroid The point where all the MEDIANS concur (meet, intersect). a.k.a. the center of gravity. The centroid divides the medians into a 2:1 ratio.  The section of the median nearest the vertex is twice as long as the section near the midpoint of the triangle's side.  Acute – inside Right – inside Obtuse - inside 

circumcenter The point where all the PERPENDICULAR BISECTORS concur (meet, intersect). The point of concurrence is the center of a circumscribed circle about the triangle. Acute – inside Right – on Obtuse - outside

O Alt. I Angle Bis. Cen Med. Ci Perp. Bis. To help you remember what lines go with which concurrence theorem, remember: O Alt. I Angle Bis. Cen Med. Ci Perp. Bis.

EULER LINE Euler Line: In any triangle, the circumcenter, centroid, and orthocenter are collinear (lie on the same straight line).   The collinear line upon which these three points lie is called the Euler line.  The centroid is always located between the circumcenter and the orthocenter.  The centroid is twice as close to the circumcenter as to the orthocenter.