Plane Geometry - Bruce E. Shapiro

SECTION 36. TRIANGLE CENTERS 183By a similar argument, the altitude through C is the perpendicular bisectorof A ′ B ′ , and the altitude through A is the perpendicular bisector of B ′ C ′ .By theorem 36.2, these three bisectors of the sides of triangle △A ′ B ′ C ′must meet at a common point O.Thus the altitudes of the original triangle △ABC meet at a common pointO.Figure 36.2: The orthocenter is the intersection of the three altitudes of atriangle.Figure 36.3: The three medians of a triangle all meet at the centroid of thetriangle.Definition 36.5 A median of a triangle is a line segment whose endpointsare one vertex and the midpoint of the side opposite that vertex.Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.