Let there be a square $ABCD$. Points $E$ and $F$ are on sides $(BC)$ and $(AB)$ such that $BF=CE$. LInes $AE$ and $CF$ intersect in point $G$. Prove that $EF$ and $DG$ are perpendicular.
Source: Moldova EGMO TST 2023
Tags: geometry
Let there be a square $ABCD$. Points $E$ and $F$ are on sides $(BC)$ and $(AB)$ such that $BF=CE$. LInes $AE$ and $CF$ intersect in point $G$. Prove that $EF$ and $DG$ are perpendicular.