Here is a very simple activity to intoduce students to the use of Geometer's SketchPad and an intriguing property of triangles.

There are various "centers" of a
triangle, one of which is called the Centroid.

Students may start by constructing a line segment, a second one, and a third to make a triangle.

A Median of a triangle is a line segment from a vertex to the midpoint of the opposite side. Students would now learn to construct midpoints.

Now, construct the medians.

Look where they meet! This intersection of all three medians is called the Centroid.

Do all three medians always intersect at one point? Click on the link below (you'll need the Geometer's Sketchpad software). Drag some vertices around to see - or choose to "animate" a vertice and sit back and watch!!