In the parallelogram ABCD, if M is any point of AB, then am − DM + DB equals () A. BCB. ABC. ACD. AD

In the parallelogram ABCD, if M is any point of AB, then am − DM + DB equals () A. BCB. ABC. ACD. AD

∵ am − DM + DB = am + MD + DB = AD + DB = AB, so select B

In the parallelogram ABCD, the vector AB = (2,4), the vector AC = (1,3), then the vector DB =?

AB = (2,4),AC=(1,3)
DB = DA + AB
= CB + AB ( DA= CB)
= CA + AB + AB
= -AC +2AB
= (-1,-3) + (4,8)
= (3,5)

In the parallelogram ABCD, AC is a diagonal, if the vector AB = (2,4), the vector AC = (1,3), then the vector DB =?

∵ vector ad = vector BC
Ψ vector DB = vector ab - vector ad
=Vector AB vector BC
=Vector ab - (vector AC vector AB)
=2 * vector ab - vector AC = (3,5)

It is known that, as shown in the figure, in the parallelogram ABCD, points E and F are the midpoint of AB and DC respectively

It is proved that: ∵ ABCD is a parallelogram, ∵ AB = DC, ∵ B = ∵ D, ad = BC. And ∵ points E and F are the middle points of AB and DC respectively, ∵ be = cf. in △ ade and △ CBF, AE = CF, ∵ a = ≌ CBC = ad, ≌ ade ≌ CBF (SAS). ≌ DEA = ≌ BFC