April 3rd, 2011, 08:50 AM  #1 
Newbie Joined: Oct 2010 Posts: 27 Thanks: 0  Another geometry proof
Hi, I need a help with this one: We have triangle ABC. D lies on AC and size of AC = CD. S is the point of intersection of AB and ACB angle bisector. M is midpoint of AB. Intersection of DM and CS is K. I need to help with proof that SB = KB (or that angles BSK and SKB are equal). 
January 29th, 2018, 05:59 AM  #2 
Newbie Joined: Feb 2015 From: Brazil Posts: 2 Thanks: 0 
This problem is not true for every triangle; take a triangle rectangle in C and the angles A=30º and B=60º. Then the angle BSK is equal to 105º, so the angle BKS will be less than 75º.
Last edited by skipjack; January 29th, 2018 at 02:32 PM. 
January 29th, 2018, 02:53 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,574 Thanks: 1485 
That seems to be an invalid argument, euzebio, as K would lie inside triangle ABC for your example. However, what has to be proved doesn't hold in your example anyway. 
February 4th, 2018, 10:36 AM  #4 
Newbie Joined: Feb 2015 From: Brazil Posts: 2 Thanks: 0 
Hi skipjack, I just showed a counter example. Of course it's true for some triangle. This statement is for all triangles, but I show that is not true.
Last edited by skipjack; February 4th, 2018 at 12:33 PM. 
February 4th, 2018, 12:22 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,574 Thanks: 1485 
Your counterexample is valid (SB and KB aren't equal), but the reasoning you gave is flawed, as K lies inside the triangle ABC that you described.

February 13th, 2018, 01:17 AM  #7 
Newbie Joined: Feb 2018 From: Israel Posts: 1 Thanks: 0 
Are the angles CAB and CBK equal as the diagram states? If so, it is quite simple (find the similar triangles) Last edited by daredman; February 13th, 2018 at 01:19 AM. 

Tags 
geometry, proof 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Geometry proof  Gustav  Geometry  2  April 14th, 2011 01:26 AM 
Geometry Proof  julian21  Geometry  2  September 3rd, 2010 02:05 PM 
Geometry Proof  meph1st0pheles  Geometry  2  February 9th, 2010 01:32 PM 
need help with geometry proof  Antiochus  Geometry  2  April 11th, 2009 10:57 AM 
Geometry Proof  meph1st0pheles  Applied Math  1  December 31st, 1969 04:00 PM 