Problem 2
Source: Canada Mathematical Olympiad 2007
October 1, 2008
ratiogeometry unsolvedgeometry
Problem Statement
You are given a pair of triangles for which two sides of one triangle are equal in length to two sides of the second triangle, and the triangles are similar, but not necessarily congruent. Prove that the ratio of the sides that correspond under the similarity is a number between \frac {1}{2}(\sqrt {5} \minus{} 1) and \frac {1}{2}(\sqrt {5} \plus{} 1).