Medians and Altitudes of a Triangle Section 5-3 Medians and Altitudes of a Triangle

Median A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

B C A

Centroid of the triangle The point of concurrency of the three medians of a triangle.

B C A P

Concurrency of medians of a triangle theorem The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

If P is the centroid of triangle ABC, then

altitude The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side Every triangle has three altitudes

B C A

Orthocenter of the triangle The point where the altitudes of a triangle intersect.

B C A P

Concurrency of altitudes of a triangle Theorem The lines containing the altitudes of a triangle are concurrent.