
Re: ? angle bisector of triangle divides opposite side in proportion to other 2 sides ?
Posted:
Mar 2, 1998 7:12 AM


In article <01bd4459$e104acc0$60b598ce@eileenst>, "Eileen Stevenson" <eks@worldpath.net> wrote:
> .... > Given an _arbitrary_ triangle ABC with AZ bisecting angle ABC, and lengths > labeled as shown, > length of AB = c, > length of BC = a, > length of AC = b, > length of AZ = d, > length of CZ = e; > then: > d/c = e/a. > > Please help. I am tutoring a bright HS student...
This is Euclid VI.3. It might be valuable for your student to look it up in Euclid, either in a library or else at http://thales.vismath.org/euclid/ or http://aleph0.clarku.edu/~djoyce/java/elements/elements.html or http://hydra.perseus.tufts.edu/cgibin/text?lookup=euc.+elem.+1+def.+1&vers=&display= if he likes using the Web.
Alternatively, here is Euclid's ingenious construction. Through C, draw a line parallel to ZB, to meet AB produced at W. Given that, your student may be able to think out the proof for himself.
Ken Pledger.

