In triangle ABC, AD, BE, CF are concurrent at O; through O parallels are drawn to EF, FD, DE, meeting the sides of ABC in L, M, P, Q, S, T, and the sides of DEF in L′, M′, P′, Q′, S′, T′. The two hexagons LMPQST, L′M′P′Q′S′T′ thus formed have the following properties:

(1) The sides L′M′, P′Q′, S′T′ of the latter are parallel to the sides of ABC.