This page shows how to construct the centroid of a triangle with compass and straightedge or ruler. The centroid of a triangle is the point where its medians intersect. It works by constructing the perpendicular bisectors of any two sides to find their midpoints. Then the medians are drawn, which intersect at the centroid. This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
The image below is the final drawing from the above animation.
|1||S is the midpoint of PQ||S was found by constructing the perpendicular bisector of PQ. See Constructing the perpendicular bisector of a segment for the method and proof|
|2||RS is a median of the triangle PQR||A median is a line from a vertex to the midpoint of the opposite side. See Median of a triangle.|
|3||Similarly, PT is a median of the triangle PQR||As in (1), (2).|
|4||C is the centroid of the triangle PQR||The centroid of a triangle is the point where its medians intersect. See Centroid of a triangle.|