My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

LinkBack Thread Tools Display Modes
November 10th, 2017, 08:53 AM   #1
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 06:36 PM.
zeta275 is offline  
November 10th, 2017, 07:14 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 21,105
Thanks: 2324

The theorem is called the Steiner–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.
skipjack is offline  

  My Math Forum > High School Math Forum > Geometry

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
open-topped box problem? djackson44 Calculus 1 February 15th, 2009 07:32 PM
A problem about semi-open set hyouga Real Analysis 2 May 3rd, 2007 12:02 PM

Copyright © 2019 My Math Forum. All rights reserved.