Answer :

__Given:-__ AB||DE , AB=DE; BC||EF, BC=EF

__Formula used:-__ SSS congruency rule

If all 3 sides of both triangle are equal then

Both triangles are congruent.

__Solution:-__

(1) In ABED

AB||DE

AB=DE

∴ ABED is a parallelogram

∵ If one pair of side in quadrilateral is equal and parallel

Then the quadrilateral is parallelogram.

(2) In BCFE

BC||EF

BC=EF

∴ BCEF is a parallelogram

∵ If one pair of side in quadrilateral is equal and parallel

Then the quadrilateral is parallelogram.

(3) As ABED is a parallelogram

BE||AD , BE=AD ;

As BCFE is a parallelogram

BE||CF , BE=CF ;

∴ By concluding both above statements

AD||CF and AD=CF

∴ ACFD is a parallelogram

∵ If one pair of side in quadrilateral is equal and parallel

Then the quadrilateral is parallelogram

If ACDF is a parallelogram ;

Then

AC=DF [opposite sides of parallelogram are equal ]

(4) In Δ ABC and Δ DEF

AB=DE [Given]

BC=EF [Given]

AC=DF [Proved above]

Δ ABC ≅ Δ DEF [SSS congruency rule]

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