How to construct (draw) the medians of a triangle

Medians of a Triangle

Geometry construction using a compass and straightedge

- Printable problem worksheet
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Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

After doing this	Your work should look like this
We start with the triangle PQR. The median of a triangle is a line segment linking the midpoint of a side to the opposite vertex. There are therefore three possible medians, and this shows one of them. The other two can be drawn in a similar fashion.
In the first four steps we create the perpendicular bisector of PQ. See Constructing a perpendicular bisector of a line segment. This establishes the midpoint of a side.
1. With the compass point on any vertex, set the compass width to about two thirds the length of either triangle side from that point. In this example, we pick point P and the side PQ.
2. Draw an arc above and below the selected side.
3. Without changing the compass width, place the compass point on the other end of the selected side, and make two more arcs so they intersect with the first two.
4. Draw a line between the points where the arcs cross. This will bisect the triangle side, dividing it into two equal parts. Label this point S.
We then simply draw a line from the midpoint to the opposite vertex.
5. Draw a line between S and the vertex opposite - in this case the point R.
6. Done. The blue line SR is one of the three possible medians of the triangle PQR. The other two can be constructed in a similar way

Try it yourself

Click here for a printable worksheet containing median 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.

Constructions pages on this site

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Triangle Centers

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Non-Euclidean constructions