equality of two angle bisectors lengths in a triangle leads to an isosceles triangle is a well known theorem.
The only proofs are based on using the lengths formula of angle bisectors or proving by contradiction.a direct proof,surprisingly,was recently a challenging problem.
Is a direct way to prove it( without the lengths formula) still unknown untill now?
Dear Otman,
it is strange that the Steiner–Lehmus theorem is a famous one and in a some way notorious in elementary geometry. I mean, there are a lot of proofs of the theeorem but none of them both direct and elementary (if it is direct, it is non-elementary, and if it is elementary, it is undirect).
It seems to be a reason to believe that a direct elementary proof of the theorem does not exist.
Greetings, Tadeusz
Thanks a lot professor Ostrowski !
Even elementary geometry is still providing challenges in th 21 century!
Best Regards
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