Q. 114.1( 383 Votes )

In Δ ABC an

Answer :

(i) Given that: AB = DE and

AB || DE

If two opposite sides of a quadrilateral are equal and parallel to each other, then it will be a parallelogram.

Therefore, quadrilateral ABED is a parallelogram


(ii) Again,


BC = EF and BC || EF

Therefore, quadrilateral BCEF is a parallelogram


(iii) As we had observed that ABED and BEFC are parallelograms


Therefore,


AD = BE and AD || BE


(Opposite sides of a parallelogram are equal and parallel)


And,


BE = CF and BE || CF


(Opposite sides of a parallelogram are equal and parallel)


AD = CF and AD || CF


(iv) As we had observed that one pair of opposite sides (AD and CF) of quadrilateral


ACFD are equal and parallel to each other, therefore, it is a parallelogram


(v) As ACFD is a parallelogram, therefore, the pair of opposite sides will be equal and parallel to each other


AC || DF and AC = DF


(vi) ΔABC and ΔDEF,


AB = DE (Given)

BC = EF (Given)

AC = DF (ACFD is a parallelogram)


ΔABC ΔDEF (By SSS congruence rule)

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