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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 (iv) quadrilateral ACDF is a parallelogram.

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 quadrilateral ACFD is a parallelogram

   

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To prove :  quadrilateral ACFD is a parallelogram

Proof : 

In ABED,

 AD=BE.................1(ABED is a parallelogram)    

 AD||BE .................2(ABED is a parallelogram)      

In BEFC,

 BE=CF.................3(BEFC is a parallelogram)    

 BE||CF .................4(BEFC is a parallelogram)      

From 2 and 4 , we get

   AD||CF...........................5

From 1 and 3, we get

   AD=CF...........................6

From 5 and 6, we get

 AD||CF and AD=CF

Thus, quadrilateral ACFD is a parallelogram

 

 

 

 

 

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seema garhwal

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