**All About A CENTROID
**

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, letÕs 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 Òcenter of gravity.Ó

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.

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