Question 119
Given triangles $ABC$ and $A_1B_1C_1$ with equal areas. Determine if it is always possible to construct (using a ruler and a compass) a triangle $A_2B_2C_2$ such that the triangles $A_1B_1C_1$ and $A_2B_2C_2$ are congruent, and the lines $AA_2$, $BB_2$ and $CC_2$ are parallel. (D. Tereshin)