Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Isosceles triangle enigma
Name: brian reynolds
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
I have a geometry question that has been plaguing me since I was in high school when it was given as an extra credit problem. The problem is: given a diagram that looks like an isosceles triangle the segments that are formed by the two "base" angle bisectors and the sides opposite the angles are given to be congruent in length. Given only that these segments, which happen to bisect these angles and terminate on the legs, are equal in length--prove that the triangle is indeed isosceles.


Replies:
The guys here in the lab have been puzzling over this one for days now; nobody can come up with a geometric proof. However, using trigonometry it is pretty simple: apply the Law of Sines to the two triangles formed by the angle bisectors and the apex of the main triangle.

hawley


Sorry about that. It is actually pretty complicated, but it can, indeed, be proven using law of Sines. We will continue to look for a geometric proof.

hawley



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory