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Medians of a Triangle

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex.

Math diagram

The medians of a triangle are concurrent at a point. The point of concurrency is called the centroid.

Math diagram

Example:

In the figure shown, $L N = 14$ units, $N K = 22$ units, and $K L = 34$ units. If $\bar{K M}$ is a median of the triangle, find the length of $\bar{L M}$ .

Math diagram

The fact that $\bar{K M}$ is a median tells us that $M$ must be a midpoint of $\bar{L N}$ . So, to find $L M$ , all we need to do is divide $L N$ by $2$ .

$L M = \frac{14}{2} = 7 units$

Note that this problem gives us a couple of pieces of irrelevant information. We don't need to know the values of $N K$ and $K L$ .