
Centroid of a Triangle
Geometry construction using a compass and straightedge
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 stepbystep instructions
The above animation is available as a
printable stepbystep 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
NonEuclidean constructions
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