How many medians can a triangle have?

3

A median of a triangle is a line segment drawn from one vertex of the triangle to the mid-point of the opposite side. It divides the triangle into two smaller triangles of equal area, making medians an important concept in geometry.

In any triangle, there are exactly three medians. Each median is associated with one vertex of the triangle. These medians are:

• AE from vertex A to the mid-point of side BC
• BF from vertex B to the mid-point of side AC
• CD from vertex C to the mid-point of side AB

The three medians of a triangle always intersect at a single point called the centroid. The centroid acts as the center of mass or balance point of the triangle.

To summarize, how many medians can a triangle have? Every triangle has exactly three medians, one from each vertex, ensuring a balance and symmetry within the triangle.