Centroid of a Triangle

We have learned that the centroid of a triangle can be found by finding the intersection of the medians. Construct the medians of ΔABC and verify that G is the centroid of this triangle. Then, use what you know about the centroid to find the coordinates of the point. Use the check box to check your answers.

1. Delete the medians of ΔABC. ΔDEF is the medial triangle for ΔABC since the vertices are the midpoints of ΔABC. Construct the medians for ΔDEF. What is the centroid of this triangle?

2. Delete these medians as well. Construct the medial triangle for ΔDEF and construct the medians of this new triangle. What is the centroid of this new triangle?

3. What do you think the centroid is going to be for the next medial triangle? Make a conjecture about the centroid of medial triangles.

Mindy Burcham, Created with GeoGebra