Median of a triangle

Definition

Let $ABC$ be a triangle in the Euclidean space $\mathbb{R}^n$. Let $M_A$ be the midpoint of $B$ and $C$. The median from $A$ is the segment $\{\, A + t (M_A - A) : t \in [0, 1] \,\}$ from $A$ to $M_A$. The medians from $B$ and from $C$ are defined in the same way, with the midpoints of $CA$ and of $AB$.

Remarks

Some texts call the whole line through $A$ and $M_A$ the median. The three medians meet at the centroid. See the medians meet at the centroid. Each median divides the triangle into two triangles of equal area. Apollonius's theorem gives the length of a median from the side lengths.

Explanations

L1 human

Join a corner of a triangle to the middle of the opposite side. The segment is a median. If the triangle is a thin plate of uniform material, it balances on each median.