Jernita Randolph

Centroid
of a Triangle

By
definition 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.

We
will use Geometer's Sketchpad to construct the centroid and explore its
location for various shapes of triangles.

First
lets draw a triangle ABC

Then
construct the midpoints of the segments of the triangle.

Now
lets construct the segments connecting the midpoints and the vertices of the
triangle.

The
intersection G of the three points is the centroid of triangle ABC. Now we will
construct obtuse and right triangles and observe the location of the centroid.

An
obtuse triangle

We
can see that the centroid still lies inside the triangle.

A
right triangle

As
we can see the centroid still lies inside the triangle, so we can conclude that
the centroid of any triangle, regardless of shape, will lie inside the
triangle.

Click
here to explore on your own.