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Steiner-Lehmus
10-Second Direct Proof
By
Hugh Ching
Steiner-Lehmus Theorem
 If in a triangle the two angle
bisectors drawn from vertices at
the base to the sides are of equal
length, then the triangle is
isosceles.
Steiner-Lehmus
10-Second Direct Proof
by
Founder of Post-Science Hugh Ching
(http://www.postscience.com)
 Draw two lines parallel to the base of the triangle
to form two isosceles triangles.
 The two lines must be equal.
 Otherwise,
the top line with the larger angle would be
shorter in the triangle,
but longer in the isosceles triangle.
Ching: Geometry is the deductive reduction to the perceptively
obvious with inductive generalization.
Appendix
Some Background Information
 The Steiner-Lehmus Theorem is famous; it even
has its own name and some history. It is described
in the book H.S.M. Coxeter, S.L. Greitzer - Geometry
Revisited, 1967. Jakob Steiner could be the
greatest mathematician in synthetic geometry and
was the first person to solve the problem.
 Hugh Ching, who has never missed a geometry
problem and has never had to take final
examinations in three geometry classes of three
different teachers, solved the Steiner-Lehmus
problem in high school without knowing its
popularity. After becoming the founder of Post-
Science, he is no longer understandable.

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Steiner-Lehmus Direct Proof

  • 2. Steiner-Lehmus Theorem  If in a triangle the two angle bisectors drawn from vertices at the base to the sides are of equal length, then the triangle is isosceles.
  • 3. Steiner-Lehmus 10-Second Direct Proof by Founder of Post-Science Hugh Ching (http://www.postscience.com)  Draw two lines parallel to the base of the triangle to form two isosceles triangles.  The two lines must be equal.  Otherwise, the top line with the larger angle would be shorter in the triangle, but longer in the isosceles triangle. Ching: Geometry is the deductive reduction to the perceptively obvious with inductive generalization.
  • 4. Appendix Some Background Information  The Steiner-Lehmus Theorem is famous; it even has its own name and some history. It is described in the book H.S.M. Coxeter, S.L. Greitzer - Geometry Revisited, 1967. Jakob Steiner could be the greatest mathematician in synthetic geometry and was the first person to solve the problem.  Hugh Ching, who has never missed a geometry problem and has never had to take final examinations in three geometry classes of three different teachers, solved the Steiner-Lehmus problem in high school without knowing its popularity. After becoming the founder of Post- Science, he is no longer understandable.