Build a triangle from medians?
- Judah L Schwartz
Three line segments (dotted lines) intersect at a point that divides the lengths of each of the segments in the ratio of 2 to 1. These three line segments could be the medians of a triangle. You can use the sliders to set the size of these three line segments. The changed lengths will maintain the 2:1 ratio. Try to set them so that points A and B, B and C, and C and A are joined by straight line segments. Alternatively, you can try to drag the points A,B and C to where you think the vertices of the target triangle are. When A, B and C lie on the vertices of the target triangle the angle between two segments of the same color will be 180 degrees. Can a triangle always be made this way? Can you prove it?