1. The CENTROID (G) 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.

First, to construct a Centroid I will begin with any triangle.

Next, I will find the midpoints of the sides and connect each of them to the vertex of the opposite side.

Finally, I will find the intersection of these segments. This will be the Centroid of the triangle.

While exploring the triangle and the Centroid I noticed that the centroid always remains inside the triangle, in every possible triangle (acute, obtuse, and right triangle).