Written by Sunny Yoon

Explore many shapes of triangles to find the relationships among G, H, C, and I.

Click here for a GSP investigation.

Click here for a GSP investigation.

Click here for a GSP investigation.

You can use the same GSP investigation above for an acute triangle.

Click here for a GSP investigation.

Click here for a GSP investigation.

When you change the triangle into an obtuse triangle, the orthic triangle disappears along with the centers of the orthic triangle. Let's see what happens when triangle ABC is a right triangle.

Click here for a GSP investigation.

Prove that the centroid is two-thirds the distance from each vertex to the opposite side.

This means that any two medians meet at their point two-thirds of the way from the vertex to the midpoint of the opposite side. So all three do because G is the concurrency of three medians.