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-   -   prove that angle formed at orthocenter is supplement of the angle formed at the vertx (http://mymathforum.com/geometry/262363-prove-angle-formed-orthocenter-supplement-angle-formed-vertx.html)

randomgamernerd November 16th, 2015 07:13 PM

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. :D:D

mrtwhs November 17th, 2015 04:26 AM

Quote:

Originally Posted by randomgamernerd (Post 451488)
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.)

Just chase angles around the picture. Here is one way:

$\displaystyle \angle BHC=90+ \angle HCA = 90 + 90 - \angle BAC$

Country Boy November 17th, 2015 09:03 AM

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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