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.