Here we will discuss about Medians and Altitudes of a Triangle
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
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.