Basic investigation of Medians in a Triangle
- Michael Andrejkovics
This construction shows a triangle with all three Medians constructed. You will notice that they intersect at one point, which is called the Centroid of the triangle. This point is the center of mass of the triangle. Try dragging the different vertices around and notice how that impacts the median and the location of the Centroid.
Now that you're familiar with the Centroid, consider the following questions: 1) Can you force the centroid to be outside the triangle? If not, why do you think this makes sense? 2) Form the triangle into an equilateral triangle with vertex A at the top. Take note of where the centroid is. Now, consider what would happen if you move vertex A towards the opposite side of the triangle. How do you think this would affect the position of the Centroid? Give it a try and see if your prediction was correct. If not, can you make sense of why it moved the way it did? 3) Look at the Median from A. Think of it as one line segment divided by the Centroid. Notice the length of the segment between point A and the Centroid; how does this compare to the length of the other segment between the Centroid and the midpoint of BC? Look at the Median from B and the Median from C. Observe the lengths of their respective segments. Do you see a pattern emerging? Can you make a conjecture about the ratio of these segments? Can you prove it?