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in Quadrilaterals by (47.3k points)
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In Fig., AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

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According to the question,

In quadrilateral ABED,

We have,

AB||DE and AB = DE

ABED is a parallelogram.

AD||BE and AD = BE

In quadrilateral ACFD,

We have,

AC||FD and AC = FD

ACFD is a parallelogram.

AD||CF and AD = CF

AD = BE = CF and CF||BE

In quadrilateral BCFE,

BE = CF and BE||CF.

BCFE is a parallelogram.

BC = EF and BC||EF

Hence proved.

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