# Median of a Triangle

## Definition

A line segment that joins the vertex of a triangle and the midpoint of the opposite side is called the median of the triangle.

Every vertex of a triangle can be connected with midpoint of its opposite side by a line segment and the line segment is known as a median of the triangle.

In any type of triangle, there are three vertices and three opposite sides. So, they can be connected by three line segments geometrically. Hence, it is possible every triangle has three medians.

### Example

$\Delta ABC$ is a triangle. Its vertices are $A$, $B$ and $C$ and its sides are $\overline{AB}$, $\overline{BC}$ and $\overline{CA}$.

#### First Median

Point $A$ is a vertex and its opposite side is $\overline{BC}$. The point $D$ is a midpoint on the side $\overline{BC}$.

Join the vertex $A$ and the midpoint $D$ by a line. It formed a line segment $\overline{AD}$ and it is known as a median of the triangle.

#### Second Median

Point $B$ is another vertex of the $\Delta ABC$ and $\overline{AC}$ is its opposite side. The point $E$ is the middle point on the side $\overline{AC}$.

A line segment, represented as $\overline{BE}$ is formed by joining the vertex $B$ and middle point $E$ by a line segment and it is called a median of the triangle.

#### Third Median

Point $C$ is another vertex of the triangle and its opposite side is $\overline{AB}$. The point $F$ is exact middle point of the side $\overline{AB}$.

Join the vertex $C$ and middle point $F$ by a line. It forms a line segment $\overline{CF}$ and it is known as a median of the triangle.

Thus, three medians are formed geometrically in any type of triangle. In $\Delta ABC$, the line segments $\overline{AD}$, $\overline{BE}$, and $\overline{CF}$ are three medians of the triangle.