How to Find the Centroid and Medians of a Triangle
A median is a line that goes from one corner of a triangle to the midpoint on the opposite side.
Theory
The Centroid and Medians
The medians have one common point of intersection. This point is called the centroid . The centroid divides all the medians in the ratio . This results in the following relationships:
When you want to find the centroid of a triangle, you need to draw two of the medians. You draw the medians by drawing a straight line from every corner to the midpoint on the opposite side. The intersection of these lines is the centroid.
Example 1
A triangle has the sides , and . Construct the centroid of the triangle.
Before you construct the centroid , you need to construct the triangle with the given measures. Start with the line . Set the compass’s radius to 7 and make a faint circle with center . Then, set the compass’s radius to 4 and make a faint circle with center . The corner appears as either of the intersection points between the two circles. Then you end up with the following triangle:
Then you construct the angle bisector for two of the sides. At the intersection between these, you have the incenter, which you call .
Then you find the midpoint to two of the sides and draw a straight line from each of these points to the opposite corner. The centroid of the triangle is the intersection between these two lines:
