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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
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions