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November 16th, 2015, 06:13 PM  #1 
Newbie Joined: Nov 2015 From: India Posts: 14 Thanks: 1  prove that angle formed at orthocenter is supplement of the angle formed at the vertx
I was searching for properties of orthocentre, circumcentre, incentre etc., and I came across this statement: the angle formed at the orthocenter is the supplement of the angle at the vertex (/_BAC + /_BHC = 180°). (Here ABC is a triangle where A is the vertex I am talking about and H is the orthocentre.) Can someone kindly prove it? Thanks for your help. Last edited by skipjack; November 17th, 2015 at 05:16 AM. 
November 17th, 2015, 03:26 AM  #2  
Senior Member Joined: Feb 2010 Posts: 707 Thanks: 142  Quote:
$\displaystyle \angle BHC=90+ \angle HCA = 90 + 90  \angle BAC$ Last edited by skipjack; November 17th, 2015 at 05:17 AM.  
November 17th, 2015, 08:03 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
The total of the interior angles in any quadrilateral add to 360 degrees. And, here, two of the angles are right angles.


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angle, formed, orthocenter, prove, supplement, vertx 
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