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Similar triangles with same orientation

Source: Germany 2007 - Problem 3

December 8, 2022
geometrysimilar trianglesmidpointTriangle

Problem Statement

We say that two triangles are oriented similarly if they are similar and have the same orientation. Prove that if ALT,ARM,ORT,ALT, ARM, ORT, and ULMULM are four triangles which are oriented similarly, then AA is the midpoint of the line segment OU.OU.