> 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".