Congruent triangles after several cuts
Source: Sharygin Finals 2017, Problem 8.4
August 4, 2017
geometrycongruent triangles
Problem Statement
Alex dissects a paper triangle into two triangles. Each minute after this he dissects one of obtained triangles into two triangles. After some time (at least one hour) it appeared that all obtained triangles were congruent. Find all initial triangles for which this is possible.