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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 06:13 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?

 mrtwhs November 17th, 2015 03:26 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 08:03 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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