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Topic: ? angle bisector of triangle divides opposite side in proportion to other 2 sides ?
Replies: 4   Last Post: Mar 4, 1998 10:46 AM

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 Ken.Pledger@vuw.ac.nz Posts: 1,412 Registered: 12/3/04
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.
>

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/cgi-bin/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.

Date Subject Author
2/28/98 Eileen Stevenson
2/28/98 John Conway
2/28/98 Alan Lipp
3/2/98 Ken.Pledger@vuw.ac.nz
3/4/98 John & Teresa Egge