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

 Messages: [ Previous | Next ]
 Barry Wolk Posts: 42 Registered: 12/6/04
Re: feet of altitudes and angles
Posted: Nov 27, 1997 9:12 PM

> 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

Date Subject Author
11/27/97 Annie Fetter
11/27/97 Mike de Villiers
11/27/97 Floor van Lamoen
11/27/97 Barry Wolk
11/28/97 John Conway
12/1/97 Michael Keyton