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Prove that there exists a plane for congruent triangles

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September 23, 2010
geometrycongruent trianglesprojectionIMO Shortlist

Problem Statement

Given two congruent triangles A1A2A3A_1A_2A_3 and B1B2B3B_1B_2B_3 (AiAk=BiBkA_iA_k = B_iB_k), prove that there exists a plane such that the orthogonal projections of these triangles onto it are congruent and equally oriented.
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