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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.
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions