Medians of a Triangle
Geometry construction using a compass and straightedge

This page shows how to construct the medians of a triangle with compass and straightedge or ruler. A triangle has three medians. They are lines linking a vertex to the midpoint of the opposite side. We first find the midpoint, then draw the median.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Proof

  Argument Reason
1 S is the midpoint of PQ By construction. See Perpendicular bisector of a line segment with compass and straightedge for method and proof.
2 RS is a median of the triangle PQR A triangle median is a line segment linking a vertex with the midpoint of the opposite side.
The other two medians from Q,P are proven in a similar way

  - Q.E.D

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

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Tangents

Ellipses

Polygons

Non-Euclidean constructions

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