Constructing the centroid of a triangle

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Centroid of a Triangle - Construction

Click here for a printable centroid construction worksheet

This demonstration shows how to construct a centroid of a triangle using only a compass and straight edge. See "Introduction to Euclidean Constructions" We start with a triangle PQR. The result is a point defining the triangle's centroid.

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.

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The centroid of a triangle is the point where all three medians intersect. In this construction, we draw any two medians and where they cross is the centroid. It is not necessary to draw all three medians.

You should be familiar with Constructing the Medians of a Triangle

Step-by-step Instructions

First, we draw the median of the triangle through R
Step 1	Construct S, the midpoint of the line segemnt PQ. See Constructing a perpendicular bisector of a line segment
Step 2	Draw the median from the midpoint S to the opposite vertex R
Next, we draw the second median of the triangle through P
Step 3	Construct T, the midpoint of the line segemnt QR. See Constructing a perpendicular bisector of a line segment
Step 4	Draw the median from the midpoint T to the opposite vertex P
Step 5	Done. The point C where the two medians intersect is the centroid of the triangle PQR.

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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions