The centroid of a triangle divides each median into a 2:1 ratio.
In triangle DEF, DC = 40 and CM = 20.
In triangle DEF, C is the centroid and DM = 60. Find DC and CM.
A centroid of a triangle is a special point where the medians of the triangle intersect. Each median divides the triangle into two triangles with equal areas. In other words, the centroid divides each median into a 2:1 ratio, where the longer segment is the one that connects the centroid to the vertex.
Knowing that DM = 60 and that C is the centroid, we can use the 2:1 ratio to find the lengths of DC and CM.
DC: Since DC is the longer segment of the median DM, we can set up the following proportion:
DC/CM = 2/1
We can then plug in the known value of DM (60) to solve for DC:
DC = (2/3) * DM
DC = (2/3) * 60
DC = 40
CM: Once we know DC, we can find CM using the same proportion:
CM = DC / 2
CM = 40 / 2
CM = 20
Therefore, DC = 40 and CM = 20.