vectors

BOLD letters are vercors

Note: Since the opposite sides of a //gram are equal in length and are parallel, they form a pair of equal vectors

AB = DC (definition of // gram)
AE = FC (given)
∴ AB - AE = DC - FC
EB = DF ______(1)

AD = BC (definition of // gram)
AE = FC (given)
∴ AD - AE = BC - FC
ED = BF _____(2)

From (1) and (2),
EB = DF and ED = BF, with EB//DF and ED//BF,
hence BFDE is a //gram (definition of //gram)