Medians and Altitudes of Triangles Section 5.3 Medians and Altitudes of Triangles

Definitions Median – A median is a line from a vertex of a triangle to the midpoint of the opposite side of the triangle. Altitude – An altitude is a line from a vertex of a triangle that is perpendicular to the line containing the opposite side.

Centroid The medians of a triangle are concurrent at a point called the centroid. The centroid is two-thirds the distance from the vertex to the midpoint of the opposite side. Centroid Diagram

Orthocenter The altitudes of a triangle are concurrent at a point called the orthocenter. Some interesting facts about the orthocenter The orthocenter, centroid, and circumcenter are collinear. The line is called the Euler line. Theorem - Take a triangle with vertices at A, B and C, and let H be its orthocenter. The orthocenter for any of the triangles formed from three of these four points is the fourth point.

Example

Homework Pg 282 #8-12, 17-23, 45