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two triangles are divided into 4 disjoint triangles

Source: ItaMO 2010, p4

February 28, 2012
geometrytrapezoidgeometry proposed

Problem Statement

In a trapezium ABCDABCD, the sides ABAB and CDCD are parallel and the angles ∠ABC\angle ABC and ∠BAD\angle BAD are acute. Show that it is possible to divide the triangle ABCABC into 4 disjoint triangle X1...,X4X_1. . . , X_4 and the triangle ABDABD into 4 disjoint triangles Y1,...,Y4Y_1,. . . , Y_4 such that the triangles XiX_i and YiY_i are congruent for all ii.
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