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

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.

**If
you would like to see animation for an acute scalene triangle
centroid Click here**

**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.**

Centroid (G) is also known as the