> -----Original Message----- > From: firstname.lastname@example.org [mailto://owner-geometry- > email@example.com] On Behalf Of Eamon > Sent: Wednesday, June 30, 2004 7:08 AM > To: firstname.lastname@example.org > Subject: Triangle Proof II > > ABC is an ARBITRARY triangle. > D lies on BC and E lies on AC. > Prove that if AD = BE then the triangle is isosceles. > > > > > y| C > | /\ > | / \ > | / \ D > | E/ \ > | / \ > | / \ > ____|/__________________\B____ > A| x
The result is of course false. More conditions should be added.
Example: Take a non-isosceles triangle ABC. From A draw a circle of arbitrary radius cutting BC at D (plus another point). With the same radius draw a circle with B as centre, cutting AC at E (plus another point). That does it. Note, there is an abundance of such radii. All you need is to pick a length greater than the largest of the altidudes of the triangle.