▁intersect s ▁the ▁side ▁lines ▁, ▁, ▁and ▁, ▁respectively . ▁ ▁Similarly , ▁let ▁Let ▁, ▁, ▁and ▁ ▁be ▁the ▁points ▁where ▁ ▁intersect s ▁those ▁side ▁lines . ▁ ▁The ▁D roz - F ar ny ▁line ▁theorem ▁says ▁that ▁the ▁mid points ▁of ▁the ▁three ▁segments ▁, ▁, ▁and ▁ ▁are ▁col linear . ▁ ▁The ▁theorem ▁was ▁stated ▁by ▁Arnold ▁D roz - F ar ny ▁in ▁ 1 8 9 9 , ▁but ▁it ▁is ▁not ▁clear ▁whether ▁he ▁had ▁a ▁proof . ▁ ▁Go orm ag ht igh ' s ▁general ization ▁A ▁general ization ▁of ▁the ▁D roz - F ar ny ▁line ▁theorem ▁was ▁proved ▁in ▁ 1 9 3 0 ▁by ▁René ▁Go orm ag ht igh . ▁ ▁As ▁above , ▁let ▁ ▁be ▁a ▁triangle ▁with ▁vertices ▁, ▁, ▁and ▁. ▁ ▁Let ▁ ▁be ▁any ▁point ▁distinct ▁from ▁, ▁, ▁and ▁, ▁and ▁ ▁be ▁any ▁line ▁through ▁. ▁Let ▁, ▁, ▁and ▁ ▁be ▁points ▁on ▁the ▁side ▁lines ▁, ▁, ▁and ▁, ▁respectively , ▁such ▁that ▁the ▁lines ▁, ▁, ▁and ▁ ▁are ▁the ▁images ▁of ▁the ▁lines ▁, ▁, ▁and ▁, ▁respectively , ▁by ▁reflection ▁against ▁the ▁line ▁. ▁Go orm ag ht igh ' s ▁theorem ▁then ▁says ▁that ▁the ▁points ▁, ▁, ▁and ▁ ▁are ▁col linear . ▁ ▁The ▁D roz - F ar ny ▁line ▁theorem ▁is ▁a ▁special ▁case ▁of ▁this ▁result , ▁when ▁ ▁is ▁the ▁orth oc enter ▁of ▁triangle