# Medians and Altitudes of a Triangle

Here we will discuss about Medians and Altitudes of a Triangle

Median:

The straight line joining a vertex of a triangle to the midpoint of the opposite side is called a median. A triangle has three medians. Here XL, YM and ZN are medians.

A geometrical property of medians:

The three medians of a triangle are concurrent, i.e., they have a common point of intersection. This point is known as the centroid of the triangle. It divides each median into the ratio 2 : 1. Here, the three medians intersect at G.

Thus, G is the centroid of the triangle.

Also, XG : GL = 2 : 1

YG : GM= 2 : 1

and    ZG : GN = 2 : 1

Altitude:

An altitude of a triangle, with respect to (or corresponding to) a side, is the perpendicular line segment drawn to the side from the opposite vertex. XL is the altitude with respect to the side YZ.

If ∆XYZ is a right-angled triangle, right angled at Y, XY is the altitude with respect to YZand YZ is the altitude with respect to XY.

If ∆XYZ is an obtuse-angled triangle in which ∠XYZ is the obtuse angle, the altitude with respect to YZ is the line segment XM drawn perpendicular to ZY produced.