We are now going to construct the [b]medians[/b] of a triangle. Medians are lines that connect the midpoint of a triangle's side with the opposite vertex. In the triangle below, use your [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] midpoint tool to find the midpoint of each side then connect these points with the [icon]/images/ggb/toolbar/mode_segment.png[/icon]line segment tool.[br][br]If you need help, use the video but try to construct this on your own.
What do you notice about the medians?[br][br]If you make the triangle acute what changes? What about right? What about obtuse?[br][br]Do you notice anything else that is special?
The medians all intersect at the same point! This point is called the [b]centroid[/b] of the triangle and it is the center of mass of the triangle. If you cut this triangle out of cardboard and tried to balance the triangle on the tip of pencil (the pencil would be vertical and the triangle would be parallel to the floor) then you would need to put the point on the centroid to balance the triangle. It always works like this because the areas of the small triangle you made inside the large triangle are perfectly balanced around the centroid.[br][br]When you make the triangle different shapes, the centroid moves around but it always stays roughly need the center of the triangle. Centroid literally means "center-like" or "center-ish" so this make sense.[br][br]The last thing is hard to notice but if you measure the length of one side of a median over the centroid and compare it to the shorter side of the median, the long side is always twice as big. This is called the [b]2/3[/b] [b]rule[/b] because it shows that the long side of the median is 2/3's the length of the median. Use your measuring tools to show that this is true!