My Math Forum angle bisectors -open problem?

 Geometry Geometry Math Forum

 November 10th, 2017, 07:53 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 well-known 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 05:36 PM.
 November 10th, 2017, 06:14 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,708 Thanks: 1805 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 07:00 PM.

 Tags angle, bisectors, open, problem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mared Geometry 2 April 2nd, 2014 02:16 PM Hammerton Real Analysis 3 January 17th, 2013 05:29 PM djackson44 Calculus 1 February 15th, 2009 06:32 PM hyouga Real Analysis 2 May 3rd, 2007 11:02 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top