Question

How many medians are there in one triangle?
(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer 1

Hint: median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. From each vertex, one median can be drawn. A triangle has three vertices.

Complete Step by Step Solution:
A triangle has three vertices. From each vertex, one median can be drawn. So, there are three medians in a triangle.

In the above $\vartriangle ABC$, A, B and C are three vertices. From vertex A, Median AD is drawn.
From vertex B, median BE is drawn.
From vertex C, median CF is drawn.
So, AD, BE, and CF are three medians.
The point of intersection of the medians of a triangle is called the centroid. In the above triangle, G is the centroid.
The median divides the opposite side equally. So, median AD bisects BC equally, BE bisects AC equally and CF bisects AB equally.
$\therefore $BD = DC, AE = EC, AF = BF
So, any triangle has three medians.

Therefore, the correct option is (C).

Note:
All the three medians of a triangle always meet at a single point, no matter what the shape of the triangle is. Each median divides the triangle into two smaller triangles which have equal area. In fact, the three medians divide the triangle into smaller triangles of equal area.