November 10th, 2017, 08:53 AM  #1 
Newbie Joined: Nov 2017 From: Israel Posts: 1 Thanks: 0  angle bisectors open problem?
Equality of angles' bisectors' lengths in a triangle leads to an isosceles triangle is a wellknown theorem. The only proofs are based on using the lengths formula of angle bisectors or proving by contradiction. A direct proof, surprisingly, is still challenging! Is a direct way to prove it (without the lengths formula) still unknown? Last edited by skipjack; November 10th, 2017 at 06:36 PM. 
November 10th, 2017, 07:14 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
The theorem is called the Steinerâ€“Lehmus theorem. It seems somewhat artificial to require a proof that doesn't use a particular formula. Also, what exactly do you mean by a "direct" proof, given that various "standard" theorems of geometry that one might like to use in a proof are usually proved "indirectly" by contradiction? There's a geometrical proof given in this article. Do you consider it to be "direct"? Last edited by skipjack; November 10th, 2017 at 08:00 PM. 

Tags 
angle, bisectors, open, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
triangle feet of bisectors  mared  Geometry  2  April 2nd, 2014 03:16 PM 
Open Cover/Subcover Problem  Hammerton  Real Analysis  3  January 17th, 2013 06:29 PM 
opentopped box problem?  djackson44  Calculus  1  February 15th, 2009 07:32 PM 
A problem about semiopen set  hyouga  Real Analysis  2  May 3rd, 2007 12:02 PM 