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median of a triangle is a line segment joining a vertex to the opposite side's mid-point.
Let us construct a median of a triangle.

Consider a triangle $$ABC$$. To draw the median, we need to consider any vertex (suppose $$A$$) and its opposite side ($$BC$$).

The midpoint of the side $$BC$$ can be found by first constructing the perpendicular bisector (with the help of a compass) on $$BC$$ and joining the intersecting arcs.

Let $$D$$ be the mid-point of $$BC$$.

Now join the point $$D$$ and the opposite vertex $$A$$. This line segment $$AD$$ is the median of a triangle $$ABC$$. Important!
1. As there are three vertices for any triangle, every triangle has three medians, one from each vertex.

2. Thus, a median connects a vertex of a triangle to the opposite side's mid-point.

3. The medians of the triangle are concurrent as they intersect at only one point.

4. A median from the vertex divides the opposite side into two equal parts. That is, a median from any vertex meets the opposite side's mid-point.