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Constructing the medians 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 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.

Geometry construction with compass and straightedge or ruler or ruler
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 compasses' point on any vertex, set the compasses' width to any medium setting. In this example, we pick point P and the side PQ. Geometry construction with compass and straightedge or ruler or ruler
2.  Draw an arc on each side of the line. Geometry construction with compass and straightedge or ruler or ruler
3.  Without changing the compasses' width, place the compasses' point on the other end of the selected side, and make two more arcs so they intersect with the first two. Geometry construction with compass and straightedge or ruler or ruler
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. Geometry construction with compass and straightedge or ruler or ruler
We then simply draw a line from this midpoint to the opposite vertex.
5.  Draw a line between S and the vertex opposite - in this case the point R. Geometry construction with compass and straightedge or ruler or ruler

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

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