KöMaL 2022 B5252

A polyhedron $ABCA_1B_1C_1$ has six vertices. Faces $ABC$ and $A_1B_1C_1$ are triangles. The edges $AA_1$, $BB_1$ and $CC_1$ are parallel. Faces $AA_1B_1B$, $BB_1C_1C$ and $CC_1A_1A$ are trapeziums in which the diagonals intersect at points $P$, $Q$ and $R$, respectively. Show that the volumes of polyhedra $ABCPQR$ and $A_1B_1C_1PQR$ are equal.