This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.

After doing this	Your work should look like this
We start with a triangle PQR.
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
2.  Draw the median from the midpoint S to the opposite vertex R
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
4.  Draw the median from the midpoint T to the opposite vertex P
(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.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object