In the diagram above, the point H is the centroid of the triangle.
In this diagram, the centroid is labeled K. In the two triangles above,
the centroid was located in the interior of the triangle.
Here, the centroid has been labeled Z. We are assured that this is a
right triangle because the measure of one of the angles is 90 degrees. As
before, the centroid is located in the interior of the triangle.
Now, consider the following ratios:
Notice that the ratio is 2:1.
It follows that each triangle has the same area.
centroid is located in the interior of any given triangle.
three medians intersect in a single point.
is a 2:1 ratio between the measure of subdivided median.
area of each triangle within the original triangle is the same.