Problem

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Tags: geometry, similar triangles, 3D geometry, parallelepiped



Let $ABCDA'B'C'D'$ be a right parallelepiped, $E$ and $F$ the projections of $A$ on the lines $A'D$, $A'C$, respectively, and $P, Q$ the projections of $B'$ on the lines $A'C'$ and $A'C$ Prove that a) the planes $(AEF)$ and $(B'PQ)$ are parallel b) the triangles $AEF$ and $B'PQ$ are similar.