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. Use Geometer's Sketchpad (GSP) to Construct the centroid and explore its location for various shapes of triangles.
Here we have constructed a triangle, now letÕs find the midpoints of this triangle,
Next, weÕll construct line segments from each vertex to the midpoint of its opposite side and the point where each segment intersects is the centroid.
So, letÕs look at the centroid, labeled G, of different triangles,
Clearly, regardless of shape or size, the centroid is always in the center of the triangle.