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What is a Median of a Triangle?

Consider the below triangle.

We have three sides and three angles (of course, because it is a triangle). To understand the medians of a triangle, we want to you pick any vertex of the triangle. You can pick anyone you want, we are picking the vertex A. Draw a straight line from vertex A to the midpoint of the opposite side (which is the line BC). That line is one of the medians of a triangle. In simple words, a median is a straight line that joins the midpoint of one side with the opposite vertex.

A triangle will always have three medians. These three medians can be used to find the centre of the triangle. Mathematicians have given a beautiful name for this centre, they call it the "centroid" of the triangle. Let's talk about the centroid of the triangle.

Centroid

We made all three medians of the triangle. Did you notice something? All the three medians are intersecting at a point that we denoted by point G. That is the centre of the triangle, also known as centroid. Hence, the centroid is the point of intersection of the three medians. The centroid is the point, where all the mass of the triangle will lie. Not to mention that centroid is the point through which you can rotate the triangle in any direction.

The centroid divides each median into two segments, the length of the segment joining the centroid to the vertex multiplied by two is the length of the segment between the midpoint and the opposite side. For example, consider the line AM. The line can be broken into two parts, AG and GM. According to the above statement, the line AG will be twice the line GM. This is applicable for every median of any kind of triangle.

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.