Question

How many medians are there in a triangle ABC?

A) $1$
B) $2$
C) $3$
D) $4$

Answer 1

Hint: First of all, we shall learn about the median of a triangle. A median of a triangle is nothing but a line segment that joins a vertex to the midpoint of the opposite side of the vertex (i.e. a line segment divides the opposite side of a triangle into two halves). Here, a line segment is a part of a line that contains two endpoints and has a definite length.
Let us deal with this concept with an example.
Let us consider a triangle ABC, where A, B, and C are its vertices.
In the given figure, DA is the line segment joining the vertex A that divides BC into two halves.
Hence, AD is the median of the triangle ABC.

 Now, we need to find the median for the figure which is given in the question.

Complete step by step answer:
Since a median of a triangle is nothing but a line segment joining a vertex to the midpoint of the opposite side of the vertex (i.e. a line segment divides the opposite side of a triangle into two halves).
In the given figure, a line segment is joining a vertex B that divides AC into two halves.
Therefore, that line segment must be the median for this triangle ABC.
Hence, the triangle ABC contains only one median.

So, the correct answer is “Option A”.

Note: We shall learn some properties of the medians of a triangle.
All triangles must contain only three medians, one from every vertex. That is, every triangle can contain at most three medians only.
Irrespective of the shape of the triangle, the three medians always meet at a single point. That single point where every median meet is known as the centroid of the triangle.
Every median divides the triangle into two smaller triangles that possess an equal area.