# Write-up 4

## by

## Lynne Bombard

This write-up is exploring the the CENTROID of a triangle.
The CENTROID 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. This is demonstrated below.

Click here to see **GSP Construction**

In the above circle, G is the centroid. I will explore
its location for various shapes of triangles.

**Right**: In the
above constructions, you can see that for a right triangle the centroid
is always in the center of the triangle. Try and move the endpoints but
still keeping one at 90 degrees you will see that the centroid is in the
center all the time.

**Obtuse**: Also
with the obtuse triangle the centroid is always in the center. If we were
to move any vertex of the triangle we would see that the centroid is always
in the center.

**Acute**: As our
findings for the first two investigations the centroid is always in the
center of the triangle also.

To see the above explorations click here **GSP
constructions**.

**Conclusion**:
Therefore, the centroid is always in the center and never moves out of any
of the vertices of the triangle. Also we see that the ratio of the midpoint
to the centroid to the centroid to the opposite vertex from the midpoint
is 1/2. And if we switch the ratios and did the segment from the vertex
to the centroid over the centroid to the midpoint the ratio would be 2.
Finally, I looked at the area of the six triangles that are formed when
we construct the centroid. I found that the area of the six triangles constructed
area are of equal area.