data-ad-format="horizontal">



 

Constructing the centroid of a triangle

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

After doing this Your work should look like this
We start with a triangle PQR. Geometry construction with compass and straightedge or ruler or ruler
First, we draw the median of the triangle through R
1.  Construct the bisector of the line segment PQ. Label the midpoint of the line S.

See Constructing a perpendicular bisector of a line segment
Geometry construction with compass and straightedge or ruler or ruler
2.  Draw the median from the midpoint S to the opposite vertex R Geometry construction with compass and straightedge or ruler or ruler
Next, we draw the second median of the triangle through P
3.  In the same manner, construct T, the midpoint of the line segment QR. See Constructing a perpendicular bisector of a line segment Geometry construction with compass and straightedge or ruler or ruler
4.  Draw the median from the midpoint T to the opposite vertex P Geometry construction with compass and straightedge or ruler or ruler
(Optional step) Repeat for the third side. This will convince you that the three medians do in fact intersect at a single point. But two are enough to find that point.
5.  Done. The point C where the two medians intersect is the centroid of the triangle PQR. Geometry construction with compass and straightedge or ruler or ruler

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions