Question

In Δs ABC and DEF, AB||DE; BC=EF and BC||EF. Vertices A, B and C are joinedto vertices D, E and F respectively (see figure). Show that(i) ABED is a parallelogram(ii) BCFE is a parallelogram(iii) AC=DF(iv) ΔABC≅ΔDEF

Answer 1

Hey there!

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(i) ABED is a parallelogram.

Given :

△ABC and △DEF,

AB = DE, AB II DE, BC = EF and BC = EF

To Prove : ABED is a parallelogram.

Proof :

Given that AB = DE and AB II DE

=> [One pair of opposite sides is parallel and equal.]

Hence, ABED is a parallelogram.

(ii) BCFE is a parallelogram.

Proof :

Given that BC = EF and BC II EF

=> [One pair of opposites sides is parallel and equal.]

Hence, BCFE is a parallelogram.

(iii) AC = DF

Proof :

From (i) and (ii) we get,

AD = CF and AD II CF

=> [One pair of opposite sides are equal and parallel to each other.]

Therefore, ACFD is a parallelogram.

So, AC = DF  ...........[Opposite sides of parallelogram]

(iv) △ABC ≅ △DEF

Proof :

AB = DE ........(given)

BC = EF ........(given)

AC = DF .......[proved in (iii)}

Hence, △ABC ≅ △DEF ..............[By SSS congruence rule]

Answer 2

Step-by-step explanation:

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