<Tri-2026-2304>, hint

Since PQ//BC, GQ=2/3DC=1/3 BC, GE/EC=1/3, Similarly GF/FB=1/3

Hence EF//BC. Since triangles EGQ and ECB are similar DE cuts GQ at M, midpoint of GQ

GQ=1/6BC GD=1/3AD while BD=1/2BC, triangles DGM and ADBare similar, AB//MD AB//ED

Similarly AC//FD. Finally triangles ABC and DEF are similar.