```Assignment #4
EMAT 6680 Dr. Wilson
Jamie Parker, Serkan Hekimoglu
University of Georgia```

Centers of a triangle (constructing the centroid)

In this assignment, we are to construct the centroid of a triangle. We will be using Geometer's Sketchpad http://www.keypress.com/ for a formal demonstration from the company. To construct the centroid, we first will construct a triangle and then construct the three medians in that triangle.

During the construction, I chose three random points, (A, B, C) and connected them with segments. I found the midpoint of each side and then constructed the medians of each side by connecting each vertex to the midpoint of the opposite side. The intersection of these three segments (C) is called the centroid of this triangle.

Now we will explore what happens to the centroid (C) as the shape of the triangle changes.

You can see that no matter what shape the triangle takes on, the centroid remains inside of the acute scalene triangle.

If you would like to see animation for an obtuse scalene triangle Click here

You can see that no matter what shape the triangle takes on, the centroid remains inside of the obtuse scalene triangle.

If you would like to see animation for a right triangle Click here

You can see that no matter what shape the triangle takes on, the centroid remains inside of the right triangle.

Showing Gpoint location and it is relation with the other points:

If you would like to see animation for different triangles Click here

Centroid (G) is also known as the "Center of Gravity" of a triangle:

If you would like to see animation for different triangles Click here