MathNet 2025-part-02 — 186 problems (EN–VI) Question 12

Consider the squares $ABCD$ and $BEFG$, such that $B$ lies on the segment $AE$ and $G$ lies on the segment $BC$. Let $H$ be the intersection of the lines $DF$ and $EG$. The perpendicular from $H$ to the line $DF$ intersects the lines $AE$ and $BC$ at points $I$ and $J$, respectively. Prove that the quadrilateral $DIFJ$ is a square.
Valeriu Bărbieru