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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 (i) quadrilateral ABED is a parallelogram

Q : 10    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

            (i) quadrilateral ABED is a parallelogram

            

            

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M mansi

Given :  In \small \Delta ABC and \small \Delta DEF,  \small AB=DE,AB\parallel DE,BC=EF and    \small BC\parallel EF.

To prove :  quadrilateral ABED is a parallelogram

Proof : In ABED,    

                  AB=DE          (Given)

                 AB||DE            (Given )

Hence, quadrilateral ABED is a parallelogram.

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