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# Steiner-Lehmus Theorem

Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the "internal bisectors problem" and "Lehmus' theorem."

Angle Bisector, Isosceles Triangle, Thomsen's Figure

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## References

Abu-Saymeh, S.; Hajja, M.; and ShahAli, H. A. "Another Variation on the Steiner-Lehmus Theme." Forum. Geom. 8, 131-140, 2008. http://forumgeom.fau.edu/FG2008volume8/FG200817index.html.Altshiller-Court, N. College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd ed., rev. enl. New York: Barnes and Noble, pp. 72-73, 1952.Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 9, 1969.Coxeter, H. S. M. and Greitzer, S. L. "The Steiner-Lehmus Theorem." §1.5 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 14-16, 1967.Gardner, M. Martin Gardner's New Mathematical Diversions from Scientific American. New York: Simon and Schuster, pp. 198-199 and 206-207, 1966.Henderson, A. "The Lehmus-Steiner-Terquem Problem in Global Survey." Scripta Math. 21, 223-232 and 309-312, 1955.Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, pp. 72-73, 1975.Neuberg, J. Bibliographie du triangle et du tétraèdre. p. 337, 1923.Oxman, V. "On the Existence of Triangles with Given Lengths of One Side and Two Adjacent Angle Bisectors." Forum Geom. 4, 215-218, 2004. http://forumgeom.fau.edu/FG2004volume4/FG200425index.html.Thébault, V. "Sur le triangle isoscèle." Mathesis 44, 97, 1930.

## Referenced on Wolfram|Alpha

Steiner-Lehmus Theorem

## Cite this as:

Weisstein, Eric W. "Steiner-Lehmus Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Steiner-LehmusTheorem.html