By: Carly Cantrell



The centroid of a triangle is the common intersection of the three medians.
A median of a triangle is the segment from a vertex to the midpoint of the opposite side.


Below is one illustration of a centroid. The centroid is located in green. There are three medians, which are in pink.


Now, let’s explore the centroids for various shapes of triangles:


Equilateral Triangle:



Right Triangle:


Isosceles Triangle:

Thus far, it appears that the centroid is always located inside any given triangle. This is a fact about centroids; they are indefinitely located in the interior of any triangle.


In fact, this is always the case because the centroid acts as the “center of gravity.”

Meaning, if one were to try and balance a triangle then the balancing point is the centroid. Why is this?

When constructing the centroid, one actually creates six congruent triangles within the original triangle.

Each of these triangles has the same area. This is because the construction of a centroid is the intersection of the three medians.

The median is the line segment connecting from a midpoint to the opposite vertex.

Thus, creating triangles with the same base and height, which is why the triangles will have the same area.

The picture below shows how the centroid created six different triangles with equivalent areas.


Notice, the original triangle is EJH. Then the centroid is F and was cnstructed by the intersections of all the medians. Hence, triangles EDF and DFJ have the same base and height so they have the same area. Similarly, triangles JFI and IFJ have the same base and height because I is the midpoint, therefore these two triangles have the same area. Also, triangles EGF and HGF share the same base and height. At this point, we have three sets of two triangles that we know have the same height, so how do we know all six have the same area? Notice, the construction of one median creates two parts to a triangle with equal area. Lets look at DJH and EDH. We know that they have the same area because D is the midpoints, so they have the same base and height. We also know that in triangle DJH that JFI and FIH have the same area, therefore must also have the same area as DFE.  

For a hands-on experience, use the provided link to manipulate triangles on your own and explore the location of the centroid.



Back to Carly's Page