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median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
Let us construct a median of a triangle.
Consider a triangle \(ABC\),
To draw the median, we need to consider the desired 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 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 \(ABC\).
  • As there are three vertices for any triangle, every triangle has three medians, one from each vertex. That is, every triangle has exactly three medians.
  • Thus, a median connects a vertex of a triangle to the mid-point of the opposite side.