Question 2
Let $G$ be the centroid of $\triangle ABC$. Through $G$ draw a line parallel to $BC$ and intersecting the sides $AB$ and $AC$ at $P$ and $Q$, respectively. Let $BQ$ intersect $GC$ at $E$ and $CP$ intersect $GB$ at $F$. Prove that triangles $ABC$ and $DEF$ are similar.
Editorial source erratum: the printed statement does not define $D$. The supplied solution and diagram use $D$ as the midpoint of $BC$. The original statement above is preserved; the solution below is conditional on this intended definition. This question requires review.
Editorial source erratum: the printed statement does not define $D$. The supplied solution and diagram use $D$ as the midpoint of $BC$. The original statement above is preserved; the solution below is conditional on this intended definition. This question requires review.