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all triangles that can be split into 2 congruent pieces by 1 cut

Source: (2021 -) 2022 Dürer Math Competition Regional E+2 https://artofproblemsolving.com/community/c1621671_

November 30, 2022
combinatorial geometrycongruent trianglesgeometry

Problem Statement

Determine all triangles that can be split into two congruent pieces by one cut. A cut consists of segments P1P2P_1P_2, P2P3P_2P_3, . . . , Pn1PnP_{n-1}P_n where points P1,P2,...,PnP_1, P_2, . . . , P_n are distinct, points P1P_1 and PnP_n lie on the perimeter of the triangle and the rest of the points lie in the interior of the triangle such that the segments are disjoint except for the endpoints.