RU-ALLRUSSIAN 2009 Problem 98

Grade 9

Triangles $ABC$ and $A_1B_1C_1$ have the same area. Using compass and ruler, can we always construct triangle $A_2B_2C_2$ equal to triangle $A_1B_1C_1$ so that the lines $AA_2$ , $BB_2$ , and $CC_2$ are parallel?

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