Two non-congruent triangles are called analogous if they can be denoted as $ABC$ and $A'B'C'$ such that $AB = A'B', AC = A'C'$ and $\angle B = \angle B'$ . Do there exist three mutually analogous triangles?
Source: Sharygin Final 2007 8.6
Tags: geometry, congruent triangles, equal angles
Two non-congruent triangles are called analogous if they can be denoted as $ABC$ and $A'B'C'$ such that $AB = A'B', AC = A'C'$ and $\angle B = \angle B'$ . Do there exist three mutually analogous triangles?