It is known that ab ∥ De, BC ∥ EF in ∥ ABC and ∥ def. Then, what is the quantitative relationship between ∥ ABC and ∥ def? Prove the conclusion

equal
prove:
∵AB∥DE,BC∥EF
The quadrilateral FBDE is a parallelogram
∴∠ABC=∠DEF

As shown in the figure, ab ∥ De, BC ∥ EF

∵ de / / AB, and ∠ DOE = ∠ AOB
∴△DOE∽△AOB
So de / AB = OE / ob
Similarly, it can be proved that Fe / CB = OE / ob
∴DE/AB=FE/CB
Also ∵ def = ∠ ABC (parallel proof ∵ deo = ∠ ABO and ∵ OEF = ∠ OBC)
∴：△DEF∽△ABC（SAS）
(corner side)

Given △ ABC ≌ △ def, BC = EF, ∠ C = ∠ F, ∠ a = 54 °, ∠ B = 28 ° and ED = 9cm, calculate the degree of ∠ F and the length of AB?

∵△ABC≌△DEF,BC=EF,∠C=∠F
∴AB=DE,AC=DF,∠A=∠D,∠B=∠E
①∵∠A=54°,∠B=28°
∴∠C=180°-∠A-∠B=98°
∴,∠F=∠C=98°
②∵AB=DE,ED=9cm
∴AB=ED=9cm

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