Centroid of a Triangle

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.

Printable step-by-step instructions

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.

Proof

The image below is the final drawing from the above animation.

Argument Reason
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.

- Q.E.D

Try it yourself

Click here for a printable worksheet containing centroid construction problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions

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