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Midsegment of a Triangle
Geometry construction using a compass and straightedge

The The midsegment of a triangle is a line which links the midpoints of two sides of the triangle. See Midsegment of a triangle. This page shows how to construct (draw) the midsegment of a given triangle with compass and straightedge or ruler. This construction uses Constructing the Perpendicular Bisector of a Line Segment to find the midpoints of the sides.

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

The image below is the final drawing above.

  Argument Reason
1 EF is the perpendicular bisector of AB. By construction. For proof see Constructing the perpendicular bisector of a line segment
2 S is the midpoint of AB From (1). EF bisects AB.
3 DG is the perpendicular bisector of BC. By construction. For proof see Constructing the perpendicular bisector of a line segment
4 T is the midpoint of BC From (1). DG bisects BC.
5 ST is a midsegment of the triangle ABC. From (2),(4). By definition. A midsegment of a triangle is a line linking the midpoint of two of its sides. See Midsegment of a triangle.

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two triangle midsegment 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.

Acknowledgements

Thanks to Aaron Strand of Carmel High School, Indiana for suggesting, reviewing, and proofreading this construction

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions