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.
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.
The image below is the final drawing above.
|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.|
Thanks to Aaron Strand of Carmel High School, Indiana for suggesting, reviewing, and proofreading this construction