Euler line
Centroid-orthocenter connection line
The Euler line is a line through a triangle that passes through several important points: the orthocenter, centroid, and circumcenter.
Named for mathematician Leonhard Euler, who proved in 1765 that these three points are always collinear in any non-equilateral triangle.
In an equilateral triangle, all three points coincide, so no unique line exists.
- orthocenterTriangle altitude concurrence point
- centroidMean position of figure
- center of gravityEquilibrium point of mass
- circumcenterPerpendicular bisectors' intersection
- geometryScience of spatial relationships
plane geometry · triangle · collinearity · Euclidean geometry · concurrency · geometric proofs · circumscribed · theorem · isosceles · bisector · vertex · proof · locus · perpendicular · Cartesian coordinates · scalene · equilateral · straightedge
- Trianglestriangle, equilateral, isosceles, scalene, right triangle
- Euler
triangle geometry constructs
Euler lineincenter
Angle bisectors' intersection
circumcircle · nine-point circle · median · altitude · angle bisector