Concurrent Triangle Medians

Activity

You will use GeoGebra (link below) to study concurrence of medians of a triangle.Go toconcurrent triangle medians, and complete each step below.

(Copy and paste in browser)

http://geogebra.org/geometry

Question 1

Using the existing midpoints of each side of the triangle, create the three medians.What do you observe about the way the medians intersect?

Question 2

Place a point at the point of intersection of the three medians.Now change the positions of verticesA,B, andC, and observe how the medians change.Is there any change in the way the medians intersect?

Question 3

How might you prove your observations in Question 2 using algebra andxandy-coordinates?Briefly outline an approach using what you know about a midpoint and the slope of a line.