David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735

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The midpoint of A and B is the point on the line through A and B that is equidistant from A and B. Draw the midpoint for each pair of vertices of the triangle below.

A median is a line from a vertex of a triangle to the midpoint of the opposite side. Draw the three medians associated with the triangle below. Move the vertices of the triangle around to see how the medians change. What do you notice?

As you may have guessed, the three medians have a single point in common. This point is called the centroid of the given triangle.

The centroid divides each median into two segments in a 2 to 1 ratio. Can you explain why?