A line $d_i~(i=1,2,3)$ intersects two opposite sides of a square $ABCD$ at points $M_i$ and $N_i$. Prove that if $M_1N_1=M_2N_2=M_3N_3$, then two of the lines $d_i$ are either parallel or perpendicular.
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Tags: geometry
A line $d_i~(i=1,2,3)$ intersects two opposite sides of a square $ABCD$ at points $M_i$ and $N_i$. Prove that if $M_1N_1=M_2N_2=M_3N_3$, then two of the lines $d_i$ are either parallel or perpendicular.