Midpoint theorem (triangle)

The midpoint theorem, midsegment theorem, or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting line segment will be parallel to the third side and have half of its length. The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio.^[1]^[2]

The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.

The triangle formed by the three parallel lines through the three midpoints of sides of a triangle is called its medial triangle.

^ Clapham, Christopher; Nicholson, James (2009). The concise Oxford dictionary of mathematics: clear definitions of even the most complex mathematical terms and concepts. Oxford paperback reference (4th ed.). Oxford: Oxford Univ. Press. p. 297. ISBN 978-0-19-923594-0.
^ French, Doug (2004). Teaching and learning geometry: issues and methods in mathematical education. London; New York: Continuum. pp. 81–84. ISBN 978-0-8264-7362-2. OCLC 56658329.

[1] Clapham, Christopher; Nicholson, James (2009). The concise Oxford dictionary of mathematics: clear definitions of even the most complex mathematical terms and concepts. Oxford paperback reference (4th ed.). Oxford: Oxford Univ. Press. p. 297. ISBN 978-0-19-923594-0.

[2] French, Doug (2004). Teaching and learning geometry: issues and methods in mathematical education. London; New York: Continuum. pp. 81–84. ISBN 978-0-8264-7362-2. OCLC 56658329.

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