∵ABCD is a parallelogram.

∴∠A=∠C,AD=BC

AE = CG = BF

∴AH=CF

∴△AEH≌△CGF

∴EH=FG

In the same way, EF=HG can be obtained.

∴ quadrilateral EFGH is a parallelogram.

Eg and FH are equally divided.

6.

Prove:

Let BM⊥AC be in M,DN⊥AC be in N.

∵ Quadrilateral ABCD is a parallelogram

∴AB=DC,AD//BC

∴∠BAM=∠DCN

∠∠BMA =∠DNC = 90。

∴△BAM≌△DCN(AAS)

∴BM=DN

And ∵ Germany = BF, ∠ DNE = ∠ BMF = 90.

∴Rt△DNE≌Rt△BMF(HL)

∴∠DEN=∠BFM

∴DE//BF

∴ Quadrilateral BFDE is a parallelogram (a group of parallelograms with equal opposite sides are parallelograms)

Remember to adopt