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  • In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (v) AC = DF

Q: 11  In \small \Delta ABC and \small \Delta DEF,  \small AB=DE,AB\parallel DE,BC = EF and  \small BC\parallel EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. \small 8.22). Show that \small AC=DF

   

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It is given that AB = DE and AB || DE

We know that If one pair of opposite sides of a quadrilateral are equal and parallel to each other, then it will be a parallelogram

Therefore, quadrilateral ABED is a parallelogram.

Given that BC = EF and BC || EF

Therefore, quadrilateral BEFC is a parallelogram.

We have observed that ABED and BEFC are parallelograms, therefore

AD = BE  and AD || BE (Opposite sides of a parallelogram are equal and parallel)

BE = CF and BE || CF (Opposite sides of a parallelogram are equal and parallel)

Thus, AD = BE = CF and AD || BE || CF

∴ AD = CF and AD || CF (Lines parallel to the same line are parallel to each other)

 one pair of opposite sides (AD and CF) of quadrilateral ACFD are equal and parallel to each other, therefore, it is a parallelogram.

In ACFD,

 AC=DF (Since, ACFD is a parallelogram )

Hence proved.

Posted by

seema garhwal

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