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Any Triangle that has two equal Angle Bisectors (each measured from a Vertex to the opposite sides) is an Isosceles Triangle. This theorem is also called the Internal Bisectors Problem and Lehmus' Theorem.
See also Isosceles Triangle
References
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, p. 72, 1952.
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 9, 1969.
Coxeter, H. S. M. and Greitzer, S. L. 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.