Download Special lines in Triangles and their points of concurrency

Special lines in Triangles
and their points of
concurrency
Perpendicular bisector of a triangle:
is perpendicular to and intersects the side of a triangle at its
midpoint
Circumcenter:
the point of concurrency for perpendicular bisectors
Center of circumscribed circle
Equal distances from the circumcenter to the vertices
Perpendicular Bisectors and the
Circumcenter
Special Lines and Points…
Angle Bisectors of a Triangle:
Lines that cut the angles of a triangle into two
congruent angles.
Incenter:
The point of concurrency for the angle bisectors.
 The center of the inscribed circle
 The incenter is equidistant from the sides of
the triangle
Angle bisectors and the Centroid
Special Lines and Points…
Medians:
A line drawn from the vertex of a triangle to the
midpoint of the opposite side.
Centroid:
Point of Concurrency for the medians
 The distance from the vertex to the centroid is 2/3 the
distance to the side of the triangle
 The shorter segment of each median then is 1/3 the
distance from the vertex to the midpoint
 The shorter segment of each median is also ½ the
larger segment
Medians and the Centroid
Special Lines and Points…
Altitudes:
A line drawn from the vertex of a triangle
perpendicular to the opposite side.
Orthocenter:

Point of Concurrency for the altitudes
The orthocenter may be inside, outside, or on
the triangle
Altitudes and the Orthocenter