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Topic: feet of altitudes and angles
Replies: 5   Last Post: Dec 1, 1997 12:41 AM

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Barry Wolk

Posts: 42
Registered: 12/6/04
Re: feet of altitudes and angles
Posted: Nov 27, 1997 9:12 PM
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> Prove that the angles formed by connecting the feet of the
> altitudes of a
> triangle are themselves bisected by the altitudes.


In fact, you don't need 3 altitudes -- one is enough.

In an acute triangle ABC, let M be the point on BC such that
AM is an altitude. Let P be any point on AM, let BP meet AC
at Q, and let CP meet AB at R. Then AM bisects angle QMR,
even if BQ and CR are not altitudes.
--
Barry Wolk | Did you know that the word "pizza"
Dept of Mathematics | is a mathematical formula? It is
University of Manitoba | the volume of a circular pizza of
Winnipeg Manitoba Canada | radius "z" and thickness "a".





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