Constructing the Centroid of a Quadrilateral

ABCD is a quadrilateral. Let's construct the centroid of ABCD.

1. Construct diagonal AC.
2. Construct the centroid of ΔABC. (Remember, it's the intersection of the medians of the triangle).
3. Construct the centroid of ΔACD the same way.
** At this point, it might be helpful to hide all objects except for the two centroids that you constructed.
4. Now, construct diagonal BD.
5. Construct the centroid of ΔABD and ΔBCD.
** Again, hide all objects except for the centroids.
6. Connect opposite centroids and construct the intersection of these two segments.

This point is the centroid of the quadrilateral. Drag the points on the original quadrilateral to make sure you agree!!

Kelly Shattuck, July 17, 2008, Created with GeoGebra